Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
5420 conjugacy classes of subgroups.
The subgroup lattice has 666 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #41×C3⋊(C3⋊D3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#64367 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C32×#1010 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D3×Q8×C3⋊D3 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11724591 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11724586 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #11724582 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #11724578 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C2×#89019 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #11724566 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #11724562 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C3⋊D3×2−1+4 | — | 3 | 1 | no | maximal |
| 13 | #10596694 | — | 3 | 4 | no | maximal |
| 14 | C33×#41 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #89080 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | Q8×C3⋊(C3⋊D3) | C22 | 1 | 1 | yes | characteristic |
| 17 | #89078 | C22 | 1 | 3 | yes | complemented |
| 18 | D4×C3⋊(C3⋊D3) | C22 | 1 | 3 | yes | — |
| 19 | #89076 | C22 | 1 | 3 | yes | complemented |
| 20 | C2×C4×C3⋊(C3⋊D3) | C22 | 1 | 3 | yes | — |
| 21 | C3×Q8×C3⋊D3 | C22 | 1 | 2 | yes | complemented |
| 22 | C3×#3830 | C22 | 1 | 6 | yes | complemented |
| 23 | C3×#3828 | C22 | 1 | 3 | yes | complemented |
| 24 | C2×C3×#634 | C22 | 1 | 3 | yes | complemented |
| 25 | C32×D3×Q8 | C22 | 1 | 2 | yes | complemented |
| 26 | C32×#237 | C22 | 1 | 6 | yes | complemented |
| 27 | C32×#235 | C22 | 1 | 3 | yes | complemented |
| 28 | C2×C32×Dic6 | C22 | 1 | 3 | yes | complemented |
| 29 | #89039 | C22 | 1 | 6 | yes | — |
| 30 | C2×#6293 | C22 | 1 | 6 | yes | complemented |
| 31 | C2×#6289 | C22 | 1 | 6 | yes | — |
| 32 | #89031 | C22 | 1 | 12 | yes | complemented |
| 33 | #89029 | C22 | 1 | 6 | yes | complemented |
| 34 | #89028 | C22 | 1 | 12 | yes | complemented |
| 35 | #89026 | C22 | 1 | 1 | yes | characteristic |
| 36 | C4×D3×C3⋊D3 | C22 | 1 | 6 | yes | — |
| 37 | #89022 | C22 | 1 | 6 | yes | complemented |
| 38 | #89020 | C22 | 1 | 6 | yes | complemented |
| 39 | #89019 | C22 | 1 | 3 | yes | — |
| 40 | #89019 | C22 | 1 | 6 | yes | — |
| 41 | #89019 | C22 | 1 | 6 | yes | complemented |
| 42 | #89019 | C22 | 1 | 6 | yes | complemented |
| 43 | #89018 | C22 | 1 | 6 | yes | complemented |
| 44 | #89017 | C22 | 1 | 3 | yes | complemented |
| 45 | C3⋊D3×Dic6 | C22 | 1 | 6 | yes | complemented |
| 46 | #89015 | C22 | 1 | 3 | yes | complemented |
| 47 | D3×#634 | C22 | 1 | 6 | yes | complemented |
| 48 | C32×2−1+4 | — | 3 | 1 | no | — |
| 49 | #64367 | — | 3 | 6 | no | — |
| 50 | #64367 | — | 3 | 3 | no | — |
| 51 | #64367 | D3 | 1 | 1 | yes | characteristic, complemented |
| 52 | #41×C3⋊D3 | — | 3 | 1 | no | — |
| 53 | #41×C3⋊D3 | — | 3 | 6 | no | — |
| 54 | #41×C3⋊D3 | — | 3 | 3 | no | — |
| 55 | #41×C3⋊D3 | — | 3 | 4 | no | — |
| 56 | #41×C3⋊D3 | — | 6 | 4 | no | — |
| 57 | #64364 | — | 3 | 2 | no | — |
| 58 | #64364 | — | 3 | 3 | no | — |
| 59 | C2×Q8×C3⋊D3 | — | 3 | 2 | no | — |
| 60 | C2×Q8×C3⋊D3 | — | 3 | 3 | no | — |
| 61 | C3×#1010 | — | 3 | 4 | no | — |
| 62 | C3×#1010 | D3 | 1 | 4 | yes | complemented |
| 63 | D32×Q8 | — | 3 | 8 | no | — |
| 64 | #64316 | — | 3 | 8 | no | — |
| 65 | #64312 | — | 3 | 24 | no | — |
| 66 | #64309 | — | 3 | 24 | no | — |
| 67 | #64306 | — | 3 | 12 | no | — |
| 68 | C2×#3797 | — | 3 | 12 | no | — |
| 69 | #64297 | — | 3 | 12 | no | — |
| 70 | #64297 | — | 3 | 12 | no | — |
| 71 | C22×C3⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 72 | C2×D3×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 73 | C33×Q8 | C23 | 1 | 1 | yes | characteristic |
| 74 | C33×D4 | C23 | 1 | 3 | yes | — |
| 75 | C2×C33×C4 | C23 | 1 | 3 | yes | — |
| 76 | #6312 | C23 | 1 | 6 | yes | — |
| 77 | C2×C3⋊(C3⋊Dic3) | C23 | 1 | 3 | yes | — |
| 78 | C4⋊(C3⋊(C3⋊D3)) | C23 | 1 | 3 | yes | — |
| 79 | C4×C3⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 80 | C4×C3⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 81 | C4×C3⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 82 | C4×C3⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 83 | #6308 | C23 | 1 | 3 | yes | — |
| 84 | C3×#638 | C23 | 1 | 6 | yes | — |
| 85 | C2×C3×C3⋊Dic3 | C23 | 1 | 6 | yes | — |
| 86 | C3×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 87 | C3×C4×C3⋊D3 | C23 | 1 | 6 | yes | — |
| 88 | C3×#634 | C23 | 1 | 6 | yes | — |
| 89 | C3×#634 | C23 | 1 | 3 | yes | — |
| 90 | C32×#67 | C23 | 1 | 6 | yes | — |
| 91 | C2×C32×Dic3 | C23 | 1 | 6 | yes | — |
| 92 | C32×D12 | C23 | 1 | 1 | yes | characteristic |
| 93 | C32×C4×D3 | C23 | 1 | 6 | yes | — |
| 94 | C32×Dic6 | C23 | 1 | 6 | yes | — |
| 95 | C32×Dic6 | C23 | 1 | 3 | yes | — |
| 96 | #6293 | C23 | 1 | 12 | yes | — |
| 97 | #6293 | C23 | 1 | 6 | yes | — |
| 98 | #6292 | C23 | 1 | 6 | yes | — |
| 99 | #6291 | C23 | 1 | 6 | yes | — |
| 100 | #6290 | C23 | 1 | 2 | yes | — |
| 101 | #6289 | C23 | 1 | 12 | yes | — |
| 102 | #6289 | C23 | 1 | 6 | yes | — |
| 103 | Dic3×C3⋊D3 | C23 | 1 | 6 | yes | — |
| 104 | D3×C3⋊Dic3 | C23 | 1 | 6 | yes | — |
| 105 | D3×2−1+4 | — | 9 | 4 | no | — |
| 106 | D3×2−1+4 | — | 9 | 1 | no | — |
| 107 | C32×#41 | — | 2 | 4 | no | — |
| 108 | C32×#41 | — | 3 | 6 | no | — |
| 109 | C32×#41 | — | 3 | 3 | no | — |
| 110 | C32×#41 | C2×D3 | 1 | 4 | yes | complemented |
| 111 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 112 | C2×C32×Q8 | — | 3 | 2 | no | — |
| 113 | C2×C32×Q8 | — | 3 | 3 | no | — |
| 114 | #3832 | — | 3 | 1 | no | — |
| 115 | #3832 | — | 3 | 4 | no | — |
| 116 | #3832 | — | 3 | 3 | no | — |
| 117 | #3832 | — | 3 | 6 | no | — |
| 118 | #3832 | — | 6 | 4 | no | — |
| 119 | Q8×C3⋊D3 | — | 3 | 1 | no | — |
| 120 | Q8×C3⋊D3 | — | 3 | 4 | no | — |
| 121 | Q8×C3⋊D3 | — | 3 | 6 | no | — |
| 122 | Q8×C3⋊D3 | — | 3 | 6 | no | — |
| 123 | Q8×C3⋊D3 | — | 3 | 3 | no | — |
| 124 | Q8×C3⋊D3 | — | 3 | 6 | no | — |
| 125 | Q8×C3⋊D3 | — | 3 | 6 | no | — |
| 126 | Q8×C3⋊D3 | — | 6 | 4 | no | — |
| 127 | Q8×C3⋊D3 | C2×D3 | 1 | 2 | yes | complemented |
| 128 | #3830 | — | 3 | 3 | no | — |
| 129 | #3830 | — | 3 | 12 | no | — |
| 130 | #3830 | — | 3 | 6 | no | — |
| 131 | #3830 | — | 3 | 12 | no | — |
| 132 | #3830 | — | 3 | 3 | no | — |
| 133 | #3830 | — | 6 | 12 | no | — |
| 134 | #3830 | C2×D3 | 1 | 6 | yes | complemented |
| 135 | D4×C3⋊D3 | — | 3 | 3 | no | — |
| 136 | D4×C3⋊D3 | — | 3 | 12 | no | — |
| 137 | D4×C3⋊D3 | — | 3 | 6 | no | — |
| 138 | D4×C3⋊D3 | — | 3 | 1 | no | — |
| 139 | D4×C3⋊D3 | — | 6 | 12 | no | — |
| 140 | #3828 | — | 3 | 3 | no | — |
| 141 | #3828 | — | 3 | 12 | no | — |
| 142 | #3828 | — | 3 | 12 | no | — |
| 143 | #3828 | — | 3 | 6 | no | — |
| 144 | #3828 | — | 3 | 6 | no | — |
| 145 | #3828 | — | 6 | 12 | no | — |
| 146 | #3828 | C2×D3 | 1 | 3 | yes | complemented |
| 147 | C2×C4×C3⋊D3 | — | 3 | 3 | no | — |
| 148 | C2×C4×C3⋊D3 | — | 3 | 12 | no | — |
| 149 | C2×C4×C3⋊D3 | — | 3 | 6 | no | — |
| 150 | C2×C4×C3⋊D3 | — | 3 | 6 | no | — |
| 151 | C2×C4×C3⋊D3 | — | 6 | 12 | no | — |
| 152 | C2×#634 | — | 3 | 6 | no | — |
| 153 | C2×#634 | — | 3 | 6 | no | — |
| 154 | C2×#634 | C2×D3 | 1 | 3 | yes | complemented |
| 155 | C3×D3×Q8 | — | 3 | 8 | no | — |
| 156 | C3×D3×Q8 | C2×D3 | 1 | 8 | yes | complemented |
| 157 | C3×#237 | — | 3 | 24 | no | — |
| 158 | C3×#237 | C2×D3 | 1 | 24 | yes | complemented |
| 159 | C3×#235 | — | 3 | 12 | no | — |
| 160 | C3×#235 | C2×D3 | 1 | 12 | yes | complemented |
| 161 | C2×C3×Dic6 | — | 3 | 12 | no | — |
| 162 | C2×C3×Dic6 | C2×D3 | 1 | 12 | yes | complemented |
| 163 | #3811 | — | 3 | 24 | no | — |
| 164 | C2×#627 | — | 3 | 24 | no | — |
| 165 | C2×#624 | — | 3 | 24 | no | — |
| 166 | #3805 | — | 3 | 24 | no | — |
| 167 | #3804 | — | 3 | 48 | no | — |
| 168 | #3804 | — | 3 | 48 | no | — |
| 169 | #3802 | — | 3 | 4 | no | — |
| 170 | C4×D32 | — | 3 | 24 | no | — |
| 171 | #3799 | — | 3 | 24 | no | — |
| 172 | #3799 | — | 3 | 24 | no | — |
| 173 | #3798 | — | 3 | 24 | no | — |
| 174 | #3797 | — | 3 | 24 | no | — |
| 175 | #3797 | — | 3 | 12 | no | — |
| 176 | #3797 | — | 3 | 24 | no | — |
| 177 | #3797 | — | 3 | 24 | no | — |
| 178 | #3796 | — | 3 | 12 | no | — |
| 179 | #3796 | — | 3 | 12 | no | — |
| 180 | D3×Dic6 | — | 3 | 24 | no | — |
| 181 | D3×Dic6 | — | 3 | 24 | no | — |
| 182 | C22×C33 | C24 | 1 | 3 | yes | — |
| 183 | C2×C3⋊(C3⋊D3) | — | 2 | 6 | no | — |
| 184 | C2×C3⋊(C3⋊D3) | C24 | 1 | 3 | yes | — |
| 185 | C2×C3⋊(C3⋊D3) | C24 | 1 | 1 | yes | characteristic |
| 186 | C2×C3×C3⋊D3 | C24 | 1 | 2 | yes | — |
| 187 | C2×C32×D3 | C24 | 1 | 2 | yes | — |
| 188 | D3×C3⋊D3 | — | 2 | 4 | no | — |
| 189 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 190 | C33×C4 | C24 | 1 | 3 | yes | — |
| 191 | C3⋊(C3⋊Dic3) | C24 | 1 | 3 | yes | — |
| 192 | C3⋊(C3⋊Dic3) | C24 | 1 | 1 | yes | characteristic |
| 193 | C3×C3⋊Dic3 | C24 | 1 | 6 | yes | — |
| 194 | C32×Dic3 | C24 | 1 | 6 | yes | — |
| 195 | C3×2−1+4 | — | 3 | 4 | no | — |
| 196 | C3×2−1+4 | — | 9 | 1 | no | — |
| 197 | #1010 | — | 3 | 4 | no | — |
| 198 | #1010 | — | 9 | 12 | no | — |
| 199 | #1010 | — | 9 | 24 | no | — |
| 200 | #1010 | — | 9 | 6 | no | — |
| 201 | #1010 | — | 9 | 3 | no | — |
| 202 | #1010 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 203 | D3×#41 | — | 9 | 12 | no | — |
| 204 | D3×#41 | — | 9 | 24 | no | — |
| 205 | D3×#41 | — | 9 | 4 | no | — |
| 206 | D3×#41 | — | 9 | 1 | no | — |
| 207 | D3×#41 | — | 9 | 6 | no | — |
| 208 | D3×#41 | — | 9 | 3 | no | — |
| 209 | D3×#41 | — | 18 | 4 | no | — |
| 210 | #1007 | — | 9 | 12 | no | — |
| 211 | #1007 | — | 9 | 8 | no | — |
| 212 | #1007 | — | 9 | 2 | no | — |
| 213 | #1007 | — | 9 | 3 | no | — |
| 214 | C2×D3×Q8 | — | 9 | 12 | no | — |
| 215 | C2×D3×Q8 | — | 9 | 8 | no | — |
| 216 | C2×D3×Q8 | — | 9 | 2 | no | — |
| 217 | C2×D3×Q8 | — | 9 | 3 | no | — |
| 218 | C22×C3⋊D3 | — | 3 | 3 | no | — |
| 219 | C22×C3⋊D3 | — | 3 | 2 | no | — |
| 220 | C22×C3⋊D3 | — | 3 | 12 | no | — |
| 221 | C22×C3⋊D3 | — | 6 | 12 | no | — |
| 222 | C2×D32 | — | 3 | 8 | no | — |
| 223 | C32×Q8 | — | 2 | 4 | no | — |
| 224 | C32×Q8 | — | 3 | 6 | no | — |
| 225 | C32×Q8 | — | 3 | 3 | no | — |
| 226 | C32×Q8 | C22×D3 | 1 | 4 | yes | — |
| 227 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 228 | C32×D4 | — | 2 | 12 | no | — |
| 229 | C32×D4 | — | 3 | 6 | no | — |
| 230 | C32×D4 | — | 3 | 1 | no | — |
| 231 | C32×D4 | C22×D3 | 1 | 12 | yes | — |
| 232 | C32×D4 | C22×D3 | 1 | 3 | yes | — |
| 233 | C2×C32×C4 | — | 2 | 12 | no | — |
| 234 | C2×C32×C4 | — | 3 | 6 | no | — |
| 235 | C2×C32×C4 | — | 3 | 6 | no | — |
| 236 | C2×C32×C4 | C22×D3 | 1 | 12 | yes | — |
| 237 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 238 | #638 | — | 3 | 6 | no | — |
| 239 | #638 | — | 3 | 2 | no | — |
| 240 | #638 | — | 3 | 6 | no | — |
| 241 | #638 | — | 3 | 24 | no | — |
| 242 | #638 | — | 6 | 24 | no | — |
| 243 | #638 | C22×D3 | 1 | 6 | yes | — |
| 244 | C2×C3⋊Dic3 | — | 3 | 3 | no | — |
| 245 | C2×C3⋊Dic3 | — | 3 | 6 | no | — |
| 246 | C2×C3⋊Dic3 | — | 3 | 12 | no | — |
| 247 | C2×C3⋊Dic3 | — | 6 | 12 | no | — |
| 248 | C2×C3⋊Dic3 | C22×D3 | 1 | 6 | yes | — |
| 249 | C4⋊(C3⋊D3) | — | 3 | 6 | no | — |
| 250 | C4⋊(C3⋊D3) | — | 3 | 3 | no | — |
| 251 | C4⋊(C3⋊D3) | — | 3 | 12 | no | — |
| 252 | C4⋊(C3⋊D3) | — | 6 | 12 | no | — |
| 253 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 254 | C4×C3⋊D3 | — | 3 | 6 | no | — |
| 255 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 256 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 257 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 258 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 259 | C4×C3⋊D3 | — | 3 | 6 | no | — |
| 260 | C4×C3⋊D3 | — | 3 | 12 | no | — |
| 261 | C4×C3⋊D3 | — | 3 | 12 | no | — |
| 262 | C4×C3⋊D3 | — | 3 | 4 | no | — |
| 263 | C4×C3⋊D3 | — | 3 | 12 | no | — |
| 264 | C4×C3⋊D3 | — | 3 | 12 | no | — |
| 265 | C4×C3⋊D3 | — | 6 | 4 | no | — |
| 266 | C4×C3⋊D3 | — | 6 | 12 | no | — |
| 267 | C4×C3⋊D3 | — | 6 | 12 | no | — |
| 268 | C4×C3⋊D3 | — | 6 | 12 | no | — |
| 269 | C4×C3⋊D3 | C22×D3 | 1 | 6 | yes | — |
| 270 | #634 | — | 3 | 3 | no | — |
| 271 | #634 | — | 3 | 12 | no | — |
| 272 | #634 | — | 3 | 6 | no | — |
| 273 | #634 | — | 3 | 12 | no | — |
| 274 | #634 | — | 6 | 12 | no | — |
| 275 | #634 | C22×D3 | 1 | 6 | yes | — |
| 276 | #634 | C22×D3 | 1 | 3 | yes | — |
| 277 | C3×#67 | — | 3 | 24 | no | — |
| 278 | C3×#67 | C22×D3 | 1 | 24 | yes | — |
| 279 | C2×C3×Dic3 | — | 3 | 24 | no | — |
| 280 | C2×C3×Dic3 | C22×D3 | 1 | 24 | yes | — |
| 281 | C3×D12 | — | 3 | 4 | no | — |
| 282 | C3×D12 | C22×D3 | 1 | 4 | yes | — |
| 283 | C3×C4×D3 | — | 3 | 24 | no | — |
| 284 | C3×C4×D3 | C22×D3 | 1 | 24 | yes | — |
| 285 | C3×Dic6 | — | 3 | 24 | no | — |
| 286 | C3×Dic6 | — | 3 | 12 | no | — |
| 287 | C3×Dic6 | C22×D3 | 1 | 24 | yes | — |
| 288 | C3×Dic6 | C22×D3 | 1 | 12 | yes | — |
| 289 | #627 | — | 3 | 48 | no | — |
| 290 | #627 | — | 3 | 24 | no | — |
| 291 | #626 | — | 3 | 24 | no | — |
| 292 | #626 | — | 3 | 24 | no | — |
| 293 | #625 | — | 3 | 8 | no | — |
| 294 | #624 | — | 3 | 24 | no | — |
| 295 | #624 | — | 3 | 48 | no | — |
| 296 | D3×Dic3 | — | 3 | 24 | no | — |
| 297 | D3×Dic3 | — | 3 | 24 | no | — |
| 298 | C2×2−1+4 | — | 27 | 1 | no | Sylow |
| 299 | C2×C33 | — | 2 | 3 | no | — |
| 300 | C2×C33 | C25 | 1 | 1 | yes | characteristic |
| 301 | C3⋊(C3⋊D3) | — | 2 | 3 | no | — |
| 302 | C3⋊(C3⋊D3) | 2−1+4 | 1 | 2 | yes | complemented |
| 303 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 304 | C32×D3 | — | 2 | 2 | no | — |
| 305 | C3×#41 | — | 2 | 4 | no | — |
| 306 | C3×#41 | — | 3 | 24 | no | — |
| 307 | C3×#41 | — | 3 | 12 | no | — |
| 308 | C3×#41 | — | 9 | 6 | no | — |
| 309 | C3×#41 | — | 9 | 3 | no | — |
| 310 | C3×#41 | D32 | 1 | 4 | yes | complemented |
| 311 | C3×#41 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 312 | C2×C3×Q8 | — | 3 | 8 | no | — |
| 313 | C2×C3×Q8 | — | 3 | 12 | no | — |
| 314 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 315 | C2×C3×Q8 | — | 9 | 3 | no | — |
| 316 | #239 | — | 9 | 24 | no | — |
| 317 | #239 | — | 9 | 12 | no | — |
| 318 | #239 | — | 9 | 4 | no | — |
| 319 | #239 | — | 9 | 1 | no | — |
| 320 | #239 | — | 9 | 3 | no | — |
| 321 | #239 | — | 9 | 6 | no | — |
| 322 | #239 | — | 18 | 4 | no | — |
| 323 | D3×Q8 | — | 3 | 8 | no | — |
| 324 | D3×Q8 | — | 9 | 12 | no | — |
| 325 | D3×Q8 | — | 9 | 24 | no | — |
| 326 | D3×Q8 | — | 9 | 24 | no | — |
| 327 | D3×Q8 | — | 9 | 24 | no | — |
| 328 | D3×Q8 | — | 9 | 24 | no | — |
| 329 | D3×Q8 | — | 9 | 4 | no | — |
| 330 | D3×Q8 | — | 9 | 1 | no | — |
| 331 | D3×Q8 | — | 9 | 6 | no | — |
| 332 | D3×Q8 | — | 9 | 6 | no | — |
| 333 | D3×Q8 | — | 9 | 3 | no | — |
| 334 | D3×Q8 | — | 9 | 6 | no | — |
| 335 | D3×Q8 | — | 9 | 6 | no | — |
| 336 | D3×Q8 | — | 18 | 4 | no | — |
| 337 | D3×Q8 | C2×C3⋊D3 | 1 | 2 | yes | complemented |
| 338 | #237 | — | 3 | 24 | no | — |
| 339 | #237 | — | 9 | 12 | no | — |
| 340 | #237 | — | 9 | 48 | no | — |
| 341 | #237 | — | 9 | 24 | no | — |
| 342 | #237 | — | 9 | 12 | no | — |
| 343 | #237 | — | 9 | 3 | no | — |
| 344 | #237 | — | 9 | 6 | no | — |
| 345 | #237 | — | 9 | 12 | no | — |
| 346 | #237 | — | 9 | 3 | no | — |
| 347 | #237 | — | 18 | 12 | no | — |
| 348 | #237 | C2×C3⋊D3 | 1 | 6 | yes | complemented |
| 349 | D3×D4 | — | 9 | 4 | no | — |
| 350 | D3×D4 | — | 9 | 24 | no | — |
| 351 | D3×D4 | — | 9 | 12 | no | — |
| 352 | D3×D4 | — | 9 | 3 | no | — |
| 353 | D3×D4 | — | 9 | 6 | no | — |
| 354 | D3×D4 | — | 9 | 1 | no | — |
| 355 | D3×D4 | — | 18 | 12 | no | — |
| 356 | #235 | — | 3 | 12 | no | — |
| 357 | #235 | — | 9 | 24 | no | — |
| 358 | #235 | — | 9 | 24 | no | — |
| 359 | #235 | — | 9 | 48 | no | — |
| 360 | #235 | — | 9 | 12 | no | — |
| 361 | #235 | — | 9 | 3 | no | — |
| 362 | #235 | — | 9 | 12 | no | — |
| 363 | #235 | — | 9 | 6 | no | — |
| 364 | #235 | — | 9 | 6 | no | — |
| 365 | #235 | — | 18 | 12 | no | — |
| 366 | #235 | C2×C3⋊D3 | 1 | 3 | yes | complemented |
| 367 | C2×C4×D3 | — | 9 | 24 | no | — |
| 368 | C2×C4×D3 | — | 9 | 24 | no | — |
| 369 | C2×C4×D3 | — | 9 | 12 | no | — |
| 370 | C2×C4×D3 | — | 9 | 3 | no | — |
| 371 | C2×C4×D3 | — | 9 | 6 | no | — |
| 372 | C2×C4×D3 | — | 9 | 6 | no | — |
| 373 | C2×C4×D3 | — | 18 | 12 | no | — |
| 374 | C2×Dic6 | — | 3 | 12 | no | — |
| 375 | C2×Dic6 | — | 9 | 24 | no | — |
| 376 | C2×Dic6 | — | 9 | 24 | no | — |
| 377 | C2×Dic6 | — | 9 | 6 | no | — |
| 378 | C2×Dic6 | — | 9 | 6 | no | — |
| 379 | C2×Dic6 | C2×C3⋊D3 | 1 | 3 | yes | complemented |
| 380 | C22×C32 | — | 2 | 12 | no | — |
| 381 | C22×C32 | — | 3 | 2 | no | — |
| 382 | C22×C32 | C23×D3 | 1 | 12 | yes | — |
| 383 | C22×C32 | C23×D3 | 1 | 3 | yes | — |
| 384 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 385 | C2×C3⋊D3 | — | 3 | 3 | no | — |
| 386 | C2×C3⋊D3 | — | 3 | 4 | no | — |
| 387 | C2×C3⋊D3 | — | 3 | 12 | no | — |
| 388 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 389 | C2×C3⋊D3 | — | 6 | 12 | no | — |
| 390 | C2×C3⋊D3 | — | 6 | 4 | no | — |
| 391 | C2×C3⋊D3 | — | 6 | 6 | no | — |
| 392 | C2×C3⋊D3 | — | 6 | 24 | no | — |
| 393 | C2×C3⋊D3 | — | 12 | 24 | no | — |
| 394 | C2×C3⋊D3 | C23×D3 | 1 | 2 | yes | — |
| 395 | C2×C3×D3 | — | 3 | 8 | no | — |
| 396 | C2×C3×D3 | C23×D3 | 1 | 8 | yes | — |
| 397 | D32 | — | 6 | 16 | no | — |
| 398 | C32×C4 | — | 2 | 12 | no | — |
| 399 | C32×C4 | — | 2 | 4 | no | — |
| 400 | C32×C4 | — | 3 | 6 | no | — |
| 401 | C32×C4 | C23×D3 | 1 | 4 | yes | — |
| 402 | C32×C4 | C23×D3 | 1 | 12 | yes | — |
| 403 | C32×C4 | C23×D3 | 1 | 3 | yes | — |
| 404 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 405 | C3⋊Dic3 | — | 3 | 3 | no | — |
| 406 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 407 | C3⋊Dic3 | — | 3 | 12 | no | — |
| 408 | C3⋊Dic3 | — | 3 | 4 | no | — |
| 409 | C3⋊Dic3 | — | 6 | 12 | no | — |
| 410 | C3⋊Dic3 | — | 6 | 4 | no | — |
| 411 | C3⋊Dic3 | C23×D3 | 1 | 6 | yes | — |
| 412 | C3×Dic3 | — | 3 | 24 | no | — |
| 413 | C3×Dic3 | C23×D3 | 1 | 24 | yes | — |
| 414 | 2−1+4 | — | 3 | 1 | no | — |
| 415 | 2−1+4 | — | 9 | 1 | no | — |
| 416 | 2−1+4 | — | 27 | 2 | no | — |
| 417 | 2−1+4 | — | 27 | 3 | no | — |
| 418 | 2−1+4 | — | 27 | 3 | no | — |
| 419 | 2−1+4 | — | 27 | 6 | no | — |
| 420 | C2×#41 | — | 27 | 6 | no | — |
| 421 | C2×#41 | — | 27 | 3 | no | — |
| 422 | C2×#41 | — | 27 | 1 | no | — |
| 423 | C22×Q8 | — | 27 | 2 | no | — |
| 424 | C22×Q8 | — | 27 | 3 | no | — |
| 425 | C33 | C2×2−1+4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 426 | C22×D3 | — | 9 | 8 | no | — |
| 427 | C22×D3 | — | 9 | 12 | no | — |
| 428 | C22×D3 | — | 9 | 3 | no | — |
| 429 | C22×D3 | — | 9 | 2 | no | — |
| 430 | C22×D3 | — | 18 | 12 | no | — |
| 431 | C3×Q8 | — | 2 | 4 | no | — |
| 432 | C3×Q8 | — | 3 | 12 | no | — |
| 433 | C3×Q8 | — | 3 | 24 | no | — |
| 434 | C3×Q8 | — | 9 | 6 | no | — |
| 435 | C3×Q8 | — | 9 | 3 | no | — |
| 436 | C3×Q8 | C2×D32 | 1 | 4 | yes | — |
| 437 | C3×Q8 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 438 | C3×D4 | — | 2 | 12 | no | — |
| 439 | C3×D4 | — | 3 | 24 | no | — |
| 440 | C3×D4 | — | 3 | 4 | no | — |
| 441 | C3×D4 | — | 9 | 6 | no | — |
| 442 | C3×D4 | — | 9 | 1 | no | — |
| 443 | C3×D4 | C2×D32 | 1 | 12 | yes | — |
| 444 | C3×D4 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 445 | C2×C3×C4 | — | 2 | 12 | no | — |
| 446 | C2×C3×C4 | — | 3 | 24 | no | — |
| 447 | C2×C3×C4 | — | 3 | 24 | no | — |
| 448 | C2×C3×C4 | — | 9 | 6 | no | — |
| 449 | C2×C3×C4 | — | 9 | 6 | no | — |
| 450 | C2×C3×C4 | C2×D32 | 1 | 12 | yes | — |
| 451 | C2×C3×C4 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 452 | #67 | — | 3 | 24 | no | — |
| 453 | #67 | — | 9 | 24 | no | — |
| 454 | #67 | — | 9 | 8 | no | — |
| 455 | #67 | — | 9 | 24 | no | — |
| 456 | #67 | — | 9 | 6 | no | — |
| 457 | #67 | — | 9 | 2 | no | — |
| 458 | #67 | — | 9 | 6 | no | — |
| 459 | #67 | — | 18 | 24 | no | — |
| 460 | #67 | C22×C3⋊D3 | 1 | 6 | yes | — |
| 461 | C2×Dic3 | — | 3 | 24 | no | — |
| 462 | C2×Dic3 | — | 9 | 24 | no | — |
| 463 | C2×Dic3 | — | 9 | 12 | no | — |
| 464 | C2×Dic3 | — | 9 | 3 | no | — |
| 465 | C2×Dic3 | — | 9 | 6 | no | — |
| 466 | C2×Dic3 | — | 18 | 12 | no | — |
| 467 | C2×Dic3 | C22×C3⋊D3 | 1 | 6 | yes | — |
| 468 | D12 | — | 3 | 4 | no | — |
| 469 | D12 | — | 9 | 24 | no | — |
| 470 | D12 | — | 9 | 6 | no | — |
| 471 | D12 | — | 9 | 12 | no | — |
| 472 | D12 | — | 9 | 3 | no | — |
| 473 | D12 | — | 18 | 12 | no | — |
| 474 | D12 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 475 | C4×D3 | — | 3 | 24 | no | — |
| 476 | C4×D3 | — | 9 | 24 | no | — |
| 477 | C4×D3 | — | 9 | 48 | no | — |
| 478 | C4×D3 | — | 9 | 24 | no | — |
| 479 | C4×D3 | — | 9 | 6 | no | — |
| 480 | C4×D3 | — | 9 | 4 | no | — |
| 481 | C4×D3 | — | 9 | 12 | no | — |
| 482 | C4×D3 | — | 9 | 12 | no | — |
| 483 | C4×D3 | — | 9 | 12 | no | — |
| 484 | C4×D3 | — | 9 | 3 | no | — |
| 485 | C4×D3 | — | 9 | 1 | no | — |
| 486 | C4×D3 | — | 9 | 3 | no | — |
| 487 | C4×D3 | — | 9 | 3 | no | — |
| 488 | C4×D3 | — | 9 | 6 | no | — |
| 489 | C4×D3 | — | 9 | 12 | no | — |
| 490 | C4×D3 | — | 18 | 4 | no | — |
| 491 | C4×D3 | — | 18 | 12 | no | — |
| 492 | C4×D3 | — | 18 | 12 | no | — |
| 493 | C4×D3 | — | 18 | 12 | no | — |
| 494 | C4×D3 | C22×C3⋊D3 | 1 | 6 | yes | — |
| 495 | Dic6 | — | 3 | 12 | no | — |
| 496 | Dic6 | — | 3 | 24 | no | — |
| 497 | Dic6 | — | 9 | 48 | no | — |
| 498 | Dic6 | — | 9 | 24 | no | — |
| 499 | Dic6 | — | 9 | 12 | no | — |
| 500 | Dic6 | — | 9 | 3 | no | — |
| 501 | Dic6 | — | 9 | 12 | no | — |
| 502 | Dic6 | — | 9 | 6 | no | — |
| 503 | Dic6 | — | 18 | 12 | no | — |
| 504 | Dic6 | C22×C3⋊D3 | 1 | 6 | yes | — |
| 505 | Dic6 | C22×C3⋊D3 | 1 | 3 | yes | — |
| 506 | C2×C32 | — | 2 | 3 | no | — |
| 507 | C2×C32 | — | 2 | 4 | no | — |
| 508 | C2×C32 | — | 2 | 12 | no | — |
| 509 | C2×C32 | — | 4 | 12 | no | — |
| 510 | C2×C32 | — | 6 | 2 | no | — |
| 511 | C2×C32 | C24×D3 | 1 | 4 | yes | — |
| 512 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 513 | C3⋊D3 | — | 2 | 2 | no | — |
| 514 | C3⋊D3 | — | 3 | 2 | no | — |
| 515 | C3⋊D3 | — | 3 | 8 | no | — |
| 516 | C3⋊D3 | — | 6 | 8 | no | — |
| 517 | C3⋊D3 | — | 6 | 3 | no | — |
| 518 | C3⋊D3 | — | 6 | 12 | no | — |
| 519 | C3⋊D3 | — | 12 | 12 | no | — |
| 520 | C3×D3 | — | 2 | 8 | no | — |
| 521 | C3×D3 | — | 6 | 8 | no | — |
| 522 | #41 | — | 3 | 6 | no | — |
| 523 | #41 | — | 3 | 3 | no | — |
| 524 | #41 | — | 9 | 6 | no | — |
| 525 | #41 | — | 9 | 3 | no | — |
| 526 | #41 | — | 27 | 6 | no | — |
| 527 | #41 | — | 27 | 12 | no | — |
| 528 | #41 | — | 27 | 6 | no | — |
| 529 | #41 | — | 27 | 12 | no | — |
| 530 | #41 | — | 27 | 6 | no | — |
| 531 | #41 | — | 27 | 6 | no | — |
| 532 | #41 | — | 27 | 3 | no | — |
| 533 | #41 | — | 27 | 3 | no | — |
| 534 | #41 | — | 27 | 1 | no | — |
| 535 | #41 | — | 27 | 3 | no | — |
| 536 | #41 | — | 27 | 3 | no | — |
| 537 | #41 | D3×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 538 | C2×Q8 | — | 3 | 2 | no | — |
| 539 | C2×Q8 | — | 3 | 3 | no | — |
| 540 | C2×Q8 | — | 9 | 2 | no | — |
| 541 | C2×Q8 | — | 9 | 3 | no | — |
| 542 | C2×Q8 | — | 27 | 6 | no | — |
| 543 | C2×Q8 | — | 27 | 6 | no | — |
| 544 | C2×Q8 | — | 27 | 6 | no | — |
| 545 | C2×Q8 | — | 27 | 6 | no | — |
| 546 | C2×Q8 | — | 27 | 3 | no | — |
| 547 | C2×Q8 | — | 27 | 6 | no | — |
| 548 | C2×Q8 | — | 27 | 6 | no | — |
| 549 | C2×Q8 | — | 27 | 1 | no | — |
| 550 | C2×D4 | — | 27 | 6 | no | — |
| 551 | C2×D4 | — | 27 | 1 | no | — |
| 552 | C2×D4 | — | 27 | 3 | no | — |
| 553 | C22×C4 | — | 27 | 6 | no | — |
| 554 | C22×C4 | — | 27 | 6 | no | — |
| 555 | C22×C4 | — | 27 | 3 | no | — |
| 556 | C22×C3 | — | 2 | 12 | no | — |
| 557 | C22×C3 | — | 3 | 8 | no | — |
| 558 | C22×C3 | — | 9 | 2 | no | — |
| 559 | C22×C3 | C22×D32 | 1 | 12 | yes | — |
| 560 | C22×C3 | C23×C3⋊D3 | 1 | 3 | yes | — |
| 561 | C2×D3 | — | 3 | 8 | no | — |
| 562 | C2×D3 | — | 9 | 4 | no | — |
| 563 | C2×D3 | — | 9 | 1 | no | — |
| 564 | C2×D3 | — | 9 | 12 | no | — |
| 565 | C2×D3 | — | 9 | 3 | no | — |
| 566 | C2×D3 | — | 18 | 4 | no | — |
| 567 | C2×D3 | — | 18 | 12 | no | — |
| 568 | C2×D3 | — | 18 | 4 | no | — |
| 569 | C2×D3 | — | 18 | 16 | no | — |
| 570 | C2×D3 | — | 18 | 6 | no | — |
| 571 | C2×D3 | — | 18 | 24 | no | — |
| 572 | C2×D3 | — | 36 | 24 | no | — |
| 573 | C2×D3 | C23×C3⋊D3 | 1 | 2 | yes | — |
| 574 | C3×C4 | — | 2 | 12 | no | — |
| 575 | C3×C4 | — | 2 | 4 | no | — |
| 576 | C3×C4 | — | 3 | 24 | no | — |
| 577 | C3×C4 | — | 9 | 6 | no | — |
| 578 | C3×C4 | C22×D32 | 1 | 4 | yes | — |
| 579 | C3×C4 | C22×D32 | 1 | 12 | yes | — |
| 580 | C3×C4 | C23×C3⋊D3 | 1 | 3 | yes | — |
| 581 | C3×C4 | C23×C3⋊D3 | 1 | 1 | yes | characteristic |
| 582 | Dic3 | — | 3 | 24 | no | — |
| 583 | Dic3 | — | 9 | 4 | no | — |
| 584 | Dic3 | — | 9 | 12 | no | — |
| 585 | Dic3 | — | 9 | 3 | no | — |
| 586 | Dic3 | — | 9 | 1 | no | — |
| 587 | Dic3 | — | 18 | 12 | no | — |
| 588 | Dic3 | — | 18 | 4 | no | — |
| 589 | Dic3 | C23×C3⋊D3 | 1 | 6 | yes | — |
| 590 | C32 | — | 2 | 4 | no | — |
| 591 | C32 | D3×2−1+4 | 1 | 4 | yes | complemented |
| 592 | C32 | D3×2−1+4 | 1 | 1 | yes | characteristic, complemented |
| 593 | C23 | — | 27 | 2 | no | — |
| 594 | C23 | — | 27 | 3 | no | — |
| 595 | Q8 | — | 3 | 6 | no | — |
| 596 | Q8 | — | 3 | 3 | no | — |
| 597 | Q8 | — | 9 | 6 | no | — |
| 598 | Q8 | — | 9 | 3 | no | — |
| 599 | Q8 | — | 27 | 6 | no | — |
| 600 | Q8 | — | 27 | 12 | no | — |
| 601 | Q8 | — | 27 | 3 | no | — |
| 602 | Q8 | C2×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 603 | D4 | — | 3 | 6 | no | — |
| 604 | D4 | — | 3 | 1 | no | — |
| 605 | D4 | — | 9 | 6 | no | — |
| 606 | D4 | — | 9 | 1 | no | — |
| 607 | D4 | — | 27 | 6 | no | — |
| 608 | D4 | — | 27 | 6 | no | — |
| 609 | D4 | — | 27 | 2 | no | — |
| 610 | D4 | — | 27 | 6 | no | — |
| 611 | D4 | — | 27 | 3 | no | — |
| 612 | D4 | C2×D3×C3⋊D3 | 1 | 3 | yes | — |
| 613 | C2×C4 | — | 3 | 6 | no | — |
| 614 | C2×C4 | — | 3 | 6 | no | — |
| 615 | C2×C4 | — | 9 | 6 | no | — |
| 616 | C2×C4 | — | 9 | 6 | no | — |
| 617 | C2×C4 | — | 27 | 6 | no | — |
| 618 | C2×C4 | — | 27 | 12 | no | — |
| 619 | C2×C4 | — | 27 | 6 | no | — |
| 620 | C2×C4 | — | 27 | 6 | no | — |
| 621 | C2×C4 | — | 27 | 3 | no | — |
| 622 | C2×C4 | — | 27 | 3 | no | — |
| 623 | C2×C4 | — | 27 | 1 | no | — |
| 624 | C2×C4 | — | 27 | 3 | no | — |
| 625 | C2×C4 | — | 27 | 3 | no | — |
| 626 | C2×C4 | C2×D3×C3⋊D3 | 1 | 3 | yes | — |
| 627 | C2×C3 | — | 2 | 12 | no | — |
| 628 | C2×C3 | — | 2 | 3 | no | — |
| 629 | C2×C3 | — | 2 | 4 | no | — |
| 630 | C2×C3 | — | 4 | 12 | no | — |
| 631 | C2×C3 | — | 6 | 8 | no | — |
| 632 | C2×C3 | — | 18 | 2 | no | — |
| 633 | C2×C3 | C23×D32 | 1 | 4 | yes | — |
| 634 | C2×C3 | C24×C3⋊D3 | 1 | 1 | yes | characteristic |
| 635 | D3 | — | 2 | 2 | no | — |
| 636 | D3 | — | 6 | 8 | no | — |
| 637 | D3 | — | 9 | 8 | no | — |
| 638 | D3 | — | 9 | 2 | no | — |
| 639 | D3 | — | 18 | 8 | no | — |
| 640 | D3 | — | 18 | 12 | no | — |
| 641 | D3 | — | 18 | 3 | no | — |
| 642 | D3 | — | 36 | 12 | no | — |
| 643 | C22 | — | 3 | 2 | no | — |
| 644 | C22 | — | 9 | 2 | no | — |
| 645 | C22 | — | 27 | 1 | no | — |
| 646 | C22 | — | 27 | 3 | no | — |
| 647 | C22 | — | 54 | 6 | no | — |
| 648 | C22 | — | 54 | 4 | no | — |
| 649 | C22 | C22×D3×C3⋊D3 | 1 | 3 | yes | — |
| 650 | C4 | — | 3 | 6 | no | — |
| 651 | C4 | — | 9 | 6 | no | — |
| 652 | C4 | — | 27 | 3 | no | — |
| 653 | C4 | — | 27 | 1 | no | — |
| 654 | C4 | C22×D3×C3⋊D3 | 1 | 3 | yes | — |
| 655 | C4 | C22×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 656 | C3 | — | 2 | 4 | no | — |
| 657 | C3 | #10596694 | 1 | 4 | yes | complemented |
| 658 | C3 | C3⋊D3×2−1+4 | 1 | 1 | yes | characteristic, complemented |
| 659 | C2 | — | 2 | 3 | no | — |
| 660 | C2 | — | 6 | 2 | no | — |
| 661 | C2 | — | 18 | 2 | no | — |
| 662 | C2 | — | 27 | 2 | no | — |
| 663 | C2 | — | 54 | 3 | no | — |
| 664 | C2 | C23×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D3×C3⋊D3 |
| commutator, socle, cosocle | C2×C33 | C25 |
| Fitting | C33×#41 | C22 |
| hypercenter | #41 | D3×C3⋊D3 |
| hypocenter | C33 | C2×2−1+4 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #41×C3⋊(C3⋊D3) | C2 | semidirect |
| 2. C3×#64367 | C2 | semidirect |
| 3. C32×#1010 | C2 | semidirect |
| 4. D3×Q8×C3⋊D3 | C2 | semidirect |
| 5. #11724591 | C2 | semidirect |
| 6. #11724586 | C2 | semidirect |
| 7. #11724582 | C2 | semidirect |
| 8. #11724578 | C2 | semidirect |
| 9. C2×#89019 | C2 | semidirect |
| 10. #11724566 | C2 | semidirect |
| 11. #11724562 | C2 | semidirect |
| 14. C33×#41 | C22 | semidirect |
| 15. #89080 | C22 | semidirect |
| 17. #89078 | C22 | semidirect |
| 19. #89076 | C22 | semidirect |
| 21. C3×Q8×C3⋊D3 | C22 | semidirect |
| 22. C3×#3830 | C22 | semidirect |
| 23. C3×#3828 | C22 | semidirect |
| 24. C2×C3×#634 | C22 | semidirect |
| 25. C32×D3×Q8 | C22 | semidirect |
| 26. C32×#237 | C22 | semidirect |
| 27. C32×#235 | C22 | semidirect |
| 28. C2×C32×Dic6 | C22 | semidirect |
| 30. C2×#6293 | C22 | semidirect |
| 32. #89031 | C22 | semidirect |
| 33. #89029 | C22 | semidirect |
| 34. #89028 | C22 | semidirect |
| 37. #89022 | C22 | semidirect |
| 38. #89020 | C22 | semidirect |
| 41. #89019 | C22 | semidirect |
| 42. #89019 | C22 | semidirect |
| 43. #89018 | C22 | semidirect |
| 44. #89017 | C22 | semidirect |
| 45. C3⋊D3×Dic6 | C22 | semidirect |
| 46. #89015 | C22 | semidirect |
| 47. D3×#634 | C22 | semidirect |
| 51. #64367 | D3 | semidirect |
| 62. C3×#1010 | D3 | semidirect |
| 110. C32×#41 | C2×D3 | semidirect |
| 111. C32×#41 | C2×D3 | semidirect |
| 127. Q8×C3⋊D3 | C2×D3 | semidirect |
| 134. #3830 | C2×D3 | semidirect |
| 146. #3828 | C2×D3 | semidirect |
| 154. C2×#634 | C2×D3 | semidirect |
| 156. C3×D3×Q8 | C2×D3 | semidirect |
| 158. C3×#237 | C2×D3 | semidirect |
| 160. C3×#235 | C2×D3 | semidirect |
| 162. C2×C3×Dic6 | C2×D3 | semidirect |
| 202. #1010 | C3⋊D3 | semidirect |
| 302. C3⋊(C3⋊D3) | 2−1+4 | semidirect |
| 310. C3×#41 | D32 | semidirect |
| 311. C3×#41 | C2×C3⋊D3 | semidirect |
| 337. D3×Q8 | C2×C3⋊D3 | semidirect |
| 348. #237 | C2×C3⋊D3 | semidirect |
| 366. #235 | C2×C3⋊D3 | semidirect |
| 379. C2×Dic6 | C2×C3⋊D3 | semidirect |
| 425. C33 | C2×2−1+4 | semidirect |
| 537. #41 | D3×C3⋊D3 | semidirect |
| 591. C32 | D3×2−1+4 | semidirect |
| 592. C32 | D3×2−1+4 | semidirect |
| 657. C3 | #10596694 | semidirect |
| 658. C3 | C3⋊D3×2−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×C3⋊(C3⋊D3) | 2 |
| C3×#64367 | 2 |
| C32×#1010 | 2 |
| D3×Q8×C3⋊D3 | 2 |
| #11724591 | 2 |
| #11724586 | 2 |
| #11724582 | 2 |
| #11724578 | 2 |
| C2×#89019 | 2 |
| #11724566 | 2 |
| #11724562 | 2 |
| C3⋊D3×2−1+4 | 3 |
| #10596694 | 3 |