Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2943 conjugacy classes of subgroups.
The subgroup lattice has 503 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #41×#272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722639 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | Q8×((C3⋊D3)⋊C3)⋊C2 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11722517 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11722505 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #11722502 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #11722491 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C2×#88651 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #11722482 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | D3×#1010 | — | 3 | 2 | no | maximal |
| 11 | #41×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #88748 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | Q8×#272 | C22 | 1 | 1 | yes | characteristic |
| 14 | #88744 | C22 | 1 | 3 | yes | complemented |
| 15 | D4×#272 | C22 | 1 | 3 | yes | — |
| 16 | #88740 | C22 | 1 | 3 | yes | complemented |
| 17 | C2×C4×#272 | C22 | 1 | 3 | yes | — |
| 18 | Q8×(C3⋊D3)⋊C3 | C22 | 1 | 4 | yes | complemented |
| 19 | #3830⋊C3 | C22 | 1 | 12 | yes | complemented |
| 20 | #3828⋊C3 | C22 | 1 | 6 | yes | complemented |
| 21 | C2×#634⋊C3 | C22 | 1 | 6 | yes | complemented |
| 22 | #88677 | C22 | 1 | 6 | yes | — |
| 23 | C2×#6199 | C22 | 1 | 6 | yes | — |
| 24 | #88672 | C22 | 1 | 6 | yes | complemented |
| 25 | #88671 | C22 | 1 | 24 | yes | complemented |
| 26 | C2×#6196 | C22 | 1 | 6 | yes | complemented |
| 27 | #88655 | C22 | 1 | 1 | yes | characteristic |
| 28 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 6 | yes | — |
| 29 | #88652 | C22 | 1 | 12 | yes | complemented |
| 30 | #88651 | C22 | 1 | 6 | yes | — |
| 31 | #88651 | C22 | 1 | 3 | yes | — |
| 32 | #88651 | C22 | 1 | 6 | yes | complemented |
| 33 | #88651 | C22 | 1 | 6 | yes | complemented |
| 34 | #88650 | C22 | 1 | 6 | yes | complemented |
| 35 | #88649 | C22 | 1 | 6 | yes | complemented |
| 36 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 12 | yes | complemented |
| 37 | #64367 | D3 | 1 | 2 | yes | complemented |
| 38 | C3×#1010 | — | 3 | 2 | no | — |
| 39 | C3×D3×#41 | — | 3 | 2 | no | — |
| 40 | C3×D3×#41 | — | 6 | 1 | no | — |
| 41 | D32×Q8 | — | 3 | 4 | no | — |
| 42 | #64315 | — | 3 | 4 | no | — |
| 43 | D3×#237 | — | 3 | 12 | no | — |
| 44 | #64309 | — | 3 | 12 | no | — |
| 45 | D3×#235 | — | 3 | 6 | no | — |
| 46 | #64298 | — | 3 | 6 | no | — |
| 47 | #64297 | — | 3 | 6 | no | — |
| 48 | C2×D3×Dic6 | — | 3 | 6 | no | — |
| 49 | C22×#272 | C23 | 1 | 3 | yes | — |
| 50 | C2×((C3⋊D3)⋊C3)⋊C2 | C23 | 1 | 2 | yes | — |
| 51 | Q8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 52 | D4×H(3,𝔽3) | C23 | 1 | 3 | yes | — |
| 53 | C2×C4×H(3,𝔽3) | C23 | 1 | 3 | yes | — |
| 54 | #6235 | C23 | 1 | 6 | yes | — |
| 55 | C2×#1084 | C23 | 1 | 3 | yes | — |
| 56 | C4⋊#272 | C23 | 1 | 3 | yes | — |
| 57 | C4×#272 | C23 | 1 | 3 | yes | — |
| 58 | C4×#272 | C23 | 1 | 3 | yes | — |
| 59 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 60 | C4×#272 | C23 | 1 | 3 | yes | — |
| 61 | #6229 | C23 | 1 | 3 | yes | — |
| 62 | #638⋊C3 | C23 | 1 | 12 | yes | — |
| 63 | C2×(C3⋊Dic3)⋊C3 | C23 | 1 | 12 | yes | — |
| 64 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 2 | yes | — |
| 65 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 12 | yes | — |
| 66 | #634⋊C3 | C23 | 1 | 12 | yes | — |
| 67 | #634⋊C3 | C23 | 1 | 6 | yes | — |
| 68 | #6200 | C23 | 1 | 12 | yes | — |
| 69 | #6199 | C23 | 1 | 6 | yes | — |
| 70 | #6199 | C23 | 1 | 12 | yes | — |
| 71 | #6198 | C23 | 1 | 2 | yes | — |
| 72 | ((C3⋊D3)⋊C3)⋊C4 | C23 | 1 | 12 | yes | — |
| 73 | #6196 | C23 | 1 | 12 | yes | — |
| 74 | #6196 | C23 | 1 | 6 | yes | — |
| 75 | D3×2−1+4 | — | 9 | 2 | no | — |
| 76 | C2×#1010 | — | 9 | 1 | no | — |
| 77 | C32×#41 | — | 2 | 1 | no | — |
| 78 | C32×#41 | C2×D3 | 1 | 2 | yes | complemented |
| 79 | Q8×C3⋊D3 | C2×D3 | 1 | 4 | yes | complemented |
| 80 | #3830 | C2×D3 | 1 | 12 | yes | complemented |
| 81 | #3828 | C2×D3 | 1 | 6 | yes | complemented |
| 82 | C2×#634 | C2×D3 | 1 | 6 | yes | complemented |
| 83 | C3×#239 | — | 3 | 2 | no | — |
| 84 | C3×#239 | — | 6 | 1 | no | — |
| 85 | C3×D3×Q8 | — | 3 | 4 | no | — |
| 86 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 87 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 88 | C3×#237 | — | 3 | 6 | no | — |
| 89 | C3×#237 | — | 3 | 12 | no | — |
| 90 | C3×#237 | — | 6 | 3 | no | — |
| 91 | C3×D3×D4 | — | 3 | 6 | no | — |
| 92 | C3×D3×D4 | — | 6 | 3 | no | — |
| 93 | C3×#235 | — | 3 | 6 | no | — |
| 94 | C3×#235 | — | 3 | 6 | no | — |
| 95 | C3×#235 | — | 6 | 3 | no | — |
| 96 | C2×C3×C4×D3 | — | 3 | 6 | no | — |
| 97 | C2×C3×C4×D3 | — | 6 | 3 | no | — |
| 98 | C2×C3×Dic6 | — | 3 | 6 | no | — |
| 99 | D3×#67 | — | 3 | 12 | no | — |
| 100 | C2×#627 | — | 3 | 12 | no | — |
| 101 | #3805 | — | 3 | 24 | no | — |
| 102 | #3804 | — | 3 | 24 | no | — |
| 103 | #3804 | — | 3 | 12 | no | — |
| 104 | C2×D3×Dic3 | — | 3 | 12 | no | — |
| 105 | D3×D12 | — | 3 | 2 | no | — |
| 106 | C4×D32 | — | 3 | 12 | no | — |
| 107 | #3799 | — | 3 | 6 | no | — |
| 108 | #3798 | — | 3 | 12 | no | — |
| 109 | #3797 | — | 3 | 12 | no | — |
| 110 | #3796 | — | 3 | 12 | no | — |
| 111 | #3795 | — | 3 | 6 | no | — |
| 112 | #3795 | — | 3 | 12 | no | — |
| 113 | D3×Dic6 | — | 3 | 6 | no | — |
| 114 | D3×Dic6 | — | 3 | 12 | no | — |
| 115 | D3×Dic6 | — | 3 | 12 | no | — |
| 116 | D3×Dic6 | — | 3 | 12 | no | — |
| 117 | D3×Dic6 | — | 3 | 12 | no | — |
| 118 | C22×H(3,𝔽3) | C24 | 1 | 3 | yes | — |
| 119 | C2×#272 | — | 2 | 6 | no | — |
| 120 | C2×#272 | C24 | 1 | 3 | yes | — |
| 121 | C2×#272 | C24 | 1 | 1 | yes | characteristic |
| 122 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 4 | yes | — |
| 123 | ((C3⋊D3)⋊C3)⋊C2 | — | 2 | 4 | no | — |
| 124 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 125 | C4×H(3,𝔽3) | C24 | 1 | 3 | yes | — |
| 126 | #1084 | C24 | 1 | 1 | yes | characteristic |
| 127 | #1084 | C24 | 1 | 3 | yes | — |
| 128 | (C3⋊Dic3)⋊C3 | C24 | 1 | 12 | yes | — |
| 129 | C3×2−1+4 | — | 9 | 2 | no | — |
| 130 | C2×C3×#41 | — | 9 | 1 | no | — |
| 131 | #1010 | — | 3 | 2 | no | — |
| 132 | #1010 | — | 9 | 2 | no | — |
| 133 | #1010 | — | 9 | 6 | no | — |
| 134 | #1010 | — | 9 | 6 | no | — |
| 135 | #1010 | — | 9 | 6 | no | — |
| 136 | #1010 | — | 9 | 12 | no | — |
| 137 | #1010 | — | 9 | 2 | no | — |
| 138 | D3×#41 | — | 3 | 2 | no | — |
| 139 | D3×#41 | — | 6 | 1 | no | — |
| 140 | D3×#41 | — | 9 | 6 | no | — |
| 141 | D3×#41 | — | 9 | 12 | no | — |
| 142 | #1007 | — | 9 | 6 | no | — |
| 143 | #1007 | — | 9 | 4 | no | — |
| 144 | C2×D3×Q8 | — | 9 | 6 | no | — |
| 145 | C2×D3×Q8 | — | 9 | 2 | no | — |
| 146 | C2×D3×Q8 | — | 9 | 4 | no | — |
| 147 | C2×#237 | — | 9 | 6 | no | — |
| 148 | C2×#235 | — | 9 | 3 | no | — |
| 149 | C22×Dic6 | — | 9 | 3 | no | — |
| 150 | C22×C3×D3 | — | 3 | 6 | no | — |
| 151 | C22×C3×D3 | — | 6 | 3 | no | — |
| 152 | C2×D32 | — | 3 | 4 | no | — |
| 153 | C32×Q8 | — | 2 | 1 | no | — |
| 154 | C32×Q8 | C22×D3 | 1 | 2 | yes | — |
| 155 | C32×D4 | — | 2 | 3 | no | — |
| 156 | C32×D4 | C22×D3 | 1 | 6 | yes | — |
| 157 | C2×C32×C4 | — | 2 | 3 | no | — |
| 158 | C2×C32×C4 | C22×D3 | 1 | 6 | yes | — |
| 159 | #638 | C22×D3 | 1 | 12 | yes | — |
| 160 | C2×C3⋊Dic3 | C22×D3 | 1 | 12 | yes | — |
| 161 | C4⋊(C3⋊D3) | C22×D3 | 1 | 2 | yes | — |
| 162 | C4×C3⋊D3 | C22×D3 | 1 | 12 | yes | — |
| 163 | #634 | C22×D3 | 1 | 6 | yes | — |
| 164 | #634 | C22×D3 | 1 | 12 | yes | — |
| 165 | C3×#67 | — | 3 | 12 | no | — |
| 166 | C3×#67 | — | 3 | 12 | no | — |
| 167 | C3×#67 | — | 6 | 6 | no | — |
| 168 | C2×C3×Dic3 | — | 3 | 12 | no | — |
| 169 | C2×C3×Dic3 | — | 3 | 6 | no | — |
| 170 | C2×C3×Dic3 | — | 6 | 3 | no | — |
| 171 | C3×D12 | — | 3 | 2 | no | — |
| 172 | C3×D12 | — | 3 | 6 | no | — |
| 173 | C3×D12 | — | 6 | 3 | no | — |
| 174 | C3×C4×D3 | — | 3 | 12 | no | — |
| 175 | C3×C4×D3 | — | 3 | 2 | no | — |
| 176 | C3×C4×D3 | — | 3 | 6 | no | — |
| 177 | C3×C4×D3 | — | 3 | 6 | no | — |
| 178 | C3×C4×D3 | — | 3 | 6 | no | — |
| 179 | C3×C4×D3 | — | 6 | 1 | no | — |
| 180 | C3×C4×D3 | — | 6 | 3 | no | — |
| 181 | C3×C4×D3 | — | 6 | 3 | no | — |
| 182 | C3×C4×D3 | — | 6 | 3 | no | — |
| 183 | C3×Dic6 | — | 3 | 6 | no | — |
| 184 | C3×Dic6 | — | 3 | 12 | no | — |
| 185 | C3×Dic6 | — | 3 | 6 | no | — |
| 186 | C3×Dic6 | — | 6 | 3 | no | — |
| 187 | #627 | — | 3 | 24 | no | — |
| 188 | #627 | — | 3 | 12 | no | — |
| 189 | #626 | — | 3 | 4 | no | — |
| 190 | #626 | — | 3 | 12 | no | — |
| 191 | #625 | — | 3 | 12 | no | — |
| 192 | #624 | — | 3 | 12 | no | — |
| 193 | D3×Dic3 | — | 3 | 12 | no | — |
| 194 | D3×Dic3 | — | 3 | 12 | no | — |
| 195 | D3×Dic3 | — | 3 | 24 | no | — |
| 196 | C2×2−1+4 | — | 27 | 1 | no | Sylow |
| 197 | C2×H(3,𝔽3) | — | 2 | 3 | no | — |
| 198 | C2×H(3,𝔽3) | C25 | 1 | 1 | yes | characteristic |
| 199 | #272 | — | 2 | 3 | no | — |
| 200 | #272 | 2−1+4 | 1 | 2 | yes | complemented |
| 201 | (C3⋊D3)⋊C3 | — | 2 | 4 | no | — |
| 202 | C3×#41 | — | 3 | 2 | no | — |
| 203 | C3×#41 | — | 6 | 1 | no | — |
| 204 | C3×#41 | — | 9 | 6 | no | — |
| 205 | C3×#41 | — | 9 | 12 | no | — |
| 206 | C3×#41 | — | 9 | 1 | no | — |
| 207 | C3×#41 | — | 9 | 3 | no | — |
| 208 | C3×#41 | — | 9 | 3 | no | — |
| 209 | C3×#41 | D32 | 1 | 1 | yes | characteristic |
| 210 | C2×C3×Q8 | — | 9 | 6 | no | — |
| 211 | C2×C3×Q8 | — | 9 | 4 | no | — |
| 212 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 213 | C2×C3×D4 | — | 9 | 3 | no | — |
| 214 | C22×C3×C4 | — | 9 | 3 | no | — |
| 215 | C2×#67 | — | 9 | 6 | no | — |
| 216 | C22×Dic3 | — | 9 | 6 | no | — |
| 217 | #239 | — | 3 | 2 | no | — |
| 218 | #239 | — | 6 | 1 | no | — |
| 219 | #239 | — | 9 | 6 | no | — |
| 220 | #239 | — | 9 | 12 | no | — |
| 221 | D3×Q8 | — | 3 | 2 | no | — |
| 222 | D3×Q8 | — | 3 | 4 | no | — |
| 223 | D3×Q8 | — | 6 | 1 | no | — |
| 224 | D3×Q8 | — | 9 | 4 | no | — |
| 225 | D3×Q8 | — | 9 | 12 | no | — |
| 226 | D3×Q8 | — | 9 | 12 | no | — |
| 227 | D3×Q8 | — | 9 | 6 | no | — |
| 228 | D3×Q8 | — | 9 | 12 | no | — |
| 229 | D3×Q8 | — | 9 | 12 | no | — |
| 230 | D3×Q8 | — | 9 | 12 | no | — |
| 231 | #237 | — | 3 | 6 | no | — |
| 232 | #237 | — | 3 | 12 | no | — |
| 233 | #237 | — | 6 | 3 | no | — |
| 234 | #237 | — | 9 | 12 | no | — |
| 235 | #237 | — | 9 | 12 | no | — |
| 236 | #237 | — | 9 | 6 | no | — |
| 237 | #237 | — | 9 | 24 | no | — |
| 238 | #237 | — | 9 | 12 | no | — |
| 239 | #237 | — | 9 | 24 | no | — |
| 240 | D3×D4 | — | 3 | 6 | no | — |
| 241 | D3×D4 | — | 6 | 3 | no | — |
| 242 | D3×D4 | — | 9 | 2 | no | — |
| 243 | D3×D4 | — | 9 | 12 | no | — |
| 244 | #235 | — | 3 | 6 | no | — |
| 245 | #235 | — | 3 | 6 | no | — |
| 246 | #235 | — | 6 | 3 | no | — |
| 247 | #235 | — | 9 | 6 | no | — |
| 248 | #235 | — | 9 | 6 | no | — |
| 249 | #235 | — | 9 | 6 | no | — |
| 250 | #235 | — | 9 | 12 | no | — |
| 251 | #235 | — | 9 | 12 | no | — |
| 252 | #235 | — | 9 | 6 | no | — |
| 253 | #235 | — | 9 | 24 | no | — |
| 254 | C2×D12 | — | 9 | 1 | no | — |
| 255 | C2×C4×D3 | — | 3 | 6 | no | — |
| 256 | C2×C4×D3 | — | 6 | 3 | no | — |
| 257 | C2×C4×D3 | — | 9 | 6 | no | — |
| 258 | C2×C4×D3 | — | 9 | 12 | no | — |
| 259 | C2×C4×D3 | — | 9 | 12 | no | — |
| 260 | C2×Dic6 | — | 3 | 6 | no | — |
| 261 | C2×Dic6 | — | 9 | 6 | no | — |
| 262 | C2×Dic6 | — | 9 | 3 | no | — |
| 263 | C2×Dic6 | — | 9 | 6 | no | — |
| 264 | C2×Dic6 | — | 9 | 6 | no | — |
| 265 | C2×Dic6 | — | 9 | 6 | no | — |
| 266 | C2×Dic6 | — | 9 | 12 | no | — |
| 267 | C2×Dic6 | — | 9 | 6 | no | — |
| 268 | C2×Dic6 | — | 9 | 12 | no | — |
| 269 | C22×C32 | — | 2 | 3 | no | — |
| 270 | C22×C32 | C23×D3 | 1 | 6 | yes | — |
| 271 | C2×C3⋊D3 | C23×D3 | 1 | 4 | yes | — |
| 272 | C2×C3×D3 | — | 3 | 2 | no | — |
| 273 | C2×C3×D3 | — | 3 | 4 | no | — |
| 274 | C2×C3×D3 | — | 3 | 6 | no | — |
| 275 | C2×C3×D3 | — | 6 | 1 | no | — |
| 276 | C2×C3×D3 | — | 6 | 3 | no | — |
| 277 | C2×C3×D3 | — | 6 | 12 | no | — |
| 278 | C2×C3×D3 | — | 12 | 6 | no | — |
| 279 | D32 | — | 6 | 8 | no | — |
| 280 | C32×C4 | — | 2 | 3 | no | — |
| 281 | C32×C4 | — | 2 | 1 | no | — |
| 282 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 283 | C32×C4 | C23×D3 | 1 | 6 | yes | — |
| 284 | C3⋊Dic3 | C23×D3 | 1 | 12 | yes | — |
| 285 | C3×Dic3 | — | 3 | 12 | no | — |
| 286 | C3×Dic3 | — | 3 | 6 | no | — |
| 287 | C3×Dic3 | — | 3 | 2 | no | — |
| 288 | C3×Dic3 | — | 6 | 3 | no | — |
| 289 | C3×Dic3 | — | 6 | 1 | no | — |
| 290 | 2−1+4 | — | 9 | 2 | no | — |
| 291 | 2−1+4 | — | 27 | 2 | no | — |
| 292 | 2−1+4 | — | 27 | 6 | no | — |
| 293 | 2−1+4 | — | 27 | 6 | no | — |
| 294 | C2×#41 | — | 9 | 1 | no | — |
| 295 | C2×#41 | — | 27 | 3 | no | — |
| 296 | C2×#41 | — | 27 | 6 | no | — |
| 297 | C22×Q8 | — | 27 | 3 | no | — |
| 298 | C22×Q8 | — | 27 | 2 | no | — |
| 299 | H(3,𝔽3) | C2×2−1+4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 300 | C23×C3 | — | 9 | 3 | no | — |
| 301 | C22×D3 | — | 3 | 6 | no | — |
| 302 | C22×D3 | — | 6 | 3 | no | — |
| 303 | C22×D3 | — | 9 | 2 | no | — |
| 304 | C22×D3 | — | 9 | 4 | no | — |
| 305 | C3×Q8 | — | 3 | 2 | no | — |
| 306 | C3×Q8 | — | 6 | 1 | no | — |
| 307 | C3×Q8 | — | 9 | 12 | no | — |
| 308 | C3×Q8 | — | 9 | 6 | no | — |
| 309 | C3×Q8 | — | 9 | 3 | no | — |
| 310 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 311 | C3×D4 | — | 3 | 6 | no | — |
| 312 | C3×D4 | — | 6 | 3 | no | — |
| 313 | C3×D4 | — | 9 | 2 | no | — |
| 314 | C3×D4 | — | 9 | 12 | no | — |
| 315 | C3×D4 | — | 9 | 6 | no | — |
| 316 | C3×D4 | — | 9 | 3 | no | — |
| 317 | C3×D4 | C2×D32 | 1 | 3 | yes | — |
| 318 | C2×C3×C4 | — | 3 | 6 | no | — |
| 319 | C2×C3×C4 | — | 6 | 3 | no | — |
| 320 | C2×C3×C4 | — | 9 | 12 | no | — |
| 321 | C2×C3×C4 | — | 9 | 12 | no | — |
| 322 | C2×C3×C4 | — | 9 | 3 | no | — |
| 323 | C2×C3×C4 | — | 9 | 1 | no | — |
| 324 | C2×C3×C4 | — | 9 | 3 | no | — |
| 325 | C2×C3×C4 | — | 9 | 3 | no | — |
| 326 | C2×C3×C4 | — | 9 | 3 | no | — |
| 327 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 328 | #67 | — | 3 | 12 | no | — |
| 329 | #67 | — | 3 | 12 | no | — |
| 330 | #67 | — | 6 | 6 | no | — |
| 331 | #67 | — | 9 | 12 | no | — |
| 332 | #67 | — | 9 | 12 | no | — |
| 333 | #67 | — | 9 | 4 | no | — |
| 334 | #67 | — | 9 | 12 | no | — |
| 335 | C2×Dic3 | — | 3 | 6 | no | — |
| 336 | C2×Dic3 | — | 3 | 12 | no | — |
| 337 | C2×Dic3 | — | 6 | 3 | no | — |
| 338 | C2×Dic3 | — | 9 | 12 | no | — |
| 339 | C2×Dic3 | — | 9 | 6 | no | — |
| 340 | C2×Dic3 | — | 9 | 12 | no | — |
| 341 | C2×Dic3 | — | 9 | 12 | no | — |
| 342 | D12 | — | 3 | 6 | no | — |
| 343 | D12 | — | 3 | 2 | no | — |
| 344 | D12 | — | 6 | 3 | no | — |
| 345 | D12 | — | 9 | 2 | no | — |
| 346 | D12 | — | 9 | 2 | no | — |
| 347 | D12 | — | 9 | 12 | no | — |
| 348 | C4×D3 | — | 3 | 2 | no | — |
| 349 | C4×D3 | — | 3 | 6 | no | — |
| 350 | C4×D3 | — | 3 | 6 | no | — |
| 351 | C4×D3 | — | 3 | 6 | no | — |
| 352 | C4×D3 | — | 3 | 12 | no | — |
| 353 | C4×D3 | — | 6 | 1 | no | — |
| 354 | C4×D3 | — | 6 | 3 | no | — |
| 355 | C4×D3 | — | 6 | 3 | no | — |
| 356 | C4×D3 | — | 6 | 3 | no | — |
| 357 | C4×D3 | — | 9 | 12 | no | — |
| 358 | C4×D3 | — | 9 | 12 | no | — |
| 359 | C4×D3 | — | 9 | 12 | no | — |
| 360 | C4×D3 | — | 9 | 12 | no | — |
| 361 | C4×D3 | — | 9 | 24 | no | — |
| 362 | Dic6 | — | 3 | 6 | no | — |
| 363 | Dic6 | — | 3 | 6 | no | — |
| 364 | Dic6 | — | 3 | 12 | no | — |
| 365 | Dic6 | — | 6 | 3 | no | — |
| 366 | Dic6 | — | 9 | 12 | no | — |
| 367 | Dic6 | — | 9 | 6 | no | — |
| 368 | Dic6 | — | 9 | 6 | no | — |
| 369 | Dic6 | — | 9 | 12 | no | — |
| 370 | Dic6 | — | 9 | 24 | no | — |
| 371 | Dic6 | — | 9 | 12 | no | — |
| 372 | C2×C32 | — | 2 | 6 | no | — |
| 373 | C2×C32 | — | 2 | 1 | no | — |
| 374 | C2×C32 | — | 4 | 3 | no | — |
| 375 | C2×C32 | C24×D3 | 1 | 2 | yes | — |
| 376 | C3⋊D3 | — | 2 | 4 | no | — |
| 377 | C3×D3 | — | 3 | 4 | no | — |
| 378 | C3×D3 | — | 6 | 2 | no | — |
| 379 | C3×D3 | — | 6 | 4 | no | — |
| 380 | C3×D3 | — | 6 | 6 | no | — |
| 381 | C3×D3 | — | 12 | 3 | no | — |
| 382 | #41 | — | 9 | 1 | no | — |
| 383 | #41 | — | 9 | 3 | no | — |
| 384 | #41 | — | 9 | 12 | no | — |
| 385 | #41 | — | 9 | 3 | no | — |
| 386 | #41 | — | 9 | 6 | no | — |
| 387 | #41 | — | 27 | 6 | no | — |
| 388 | #41 | — | 27 | 6 | no | — |
| 389 | #41 | — | 27 | 24 | no | — |
| 390 | #41 | — | 27 | 6 | no | — |
| 391 | #41 | — | 27 | 12 | no | — |
| 392 | #41 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 393 | C2×Q8 | — | 9 | 1 | no | — |
| 394 | C2×Q8 | — | 9 | 4 | no | — |
| 395 | C2×Q8 | — | 9 | 6 | no | — |
| 396 | C2×Q8 | — | 27 | 6 | no | — |
| 397 | C2×Q8 | — | 27 | 3 | no | — |
| 398 | C2×Q8 | — | 27 | 6 | no | — |
| 399 | C2×Q8 | — | 27 | 6 | no | — |
| 400 | C2×Q8 | — | 27 | 6 | no | — |
| 401 | C2×Q8 | — | 27 | 12 | no | — |
| 402 | C2×D4 | — | 9 | 3 | no | — |
| 403 | C2×D4 | — | 27 | 1 | no | — |
| 404 | C2×D4 | — | 27 | 6 | no | — |
| 405 | C22×C4 | — | 9 | 3 | no | — |
| 406 | C22×C4 | — | 27 | 6 | no | — |
| 407 | C22×C4 | — | 27 | 6 | no | — |
| 408 | C22×C3 | — | 3 | 6 | no | — |
| 409 | C22×C3 | — | 6 | 3 | no | — |
| 410 | C22×C3 | — | 9 | 4 | no | — |
| 411 | C22×C3 | — | 9 | 1 | no | — |
| 412 | C22×C3 | — | 9 | 3 | no | — |
| 413 | C22×C3 | — | 18 | 6 | no | — |
| 414 | C22×C3 | C22×D32 | 1 | 3 | yes | — |
| 415 | C2×D3 | — | 3 | 2 | no | — |
| 416 | C2×D3 | — | 3 | 6 | no | — |
| 417 | C2×D3 | — | 3 | 4 | no | — |
| 418 | C2×D3 | — | 6 | 1 | no | — |
| 419 | C2×D3 | — | 6 | 3 | no | — |
| 420 | C2×D3 | — | 6 | 12 | no | — |
| 421 | C2×D3 | — | 9 | 4 | no | — |
| 422 | C2×D3 | — | 12 | 6 | no | — |
| 423 | C2×D3 | — | 18 | 8 | no | — |
| 424 | C2×D3 | — | 18 | 4 | no | — |
| 425 | C3×C4 | — | 3 | 6 | no | — |
| 426 | C3×C4 | — | 3 | 2 | no | — |
| 427 | C3×C4 | — | 6 | 3 | no | — |
| 428 | C3×C4 | — | 6 | 1 | no | — |
| 429 | C3×C4 | — | 9 | 12 | no | — |
| 430 | C3×C4 | — | 9 | 1 | no | — |
| 431 | C3×C4 | — | 9 | 3 | no | — |
| 432 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 433 | C3×C4 | C22×D32 | 1 | 3 | yes | — |
| 434 | Dic3 | — | 3 | 6 | no | — |
| 435 | Dic3 | — | 3 | 2 | no | — |
| 436 | Dic3 | — | 3 | 12 | no | — |
| 437 | Dic3 | — | 6 | 3 | no | — |
| 438 | Dic3 | — | 6 | 1 | no | — |
| 439 | Dic3 | — | 9 | 12 | no | — |
| 440 | C32 | — | 2 | 1 | no | — |
| 441 | C32 | D3×2−1+4 | 1 | 2 | yes | complemented |
| 442 | C23 | — | 9 | 3 | no | — |
| 443 | C23 | — | 27 | 2 | no | — |
| 444 | Q8 | — | 9 | 12 | no | — |
| 445 | Q8 | — | 9 | 6 | no | — |
| 446 | Q8 | — | 9 | 3 | no | — |
| 447 | Q8 | — | 27 | 6 | no | — |
| 448 | Q8 | — | 27 | 12 | no | — |
| 449 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 450 | D4 | — | 9 | 6 | no | — |
| 451 | D4 | — | 9 | 12 | no | — |
| 452 | D4 | — | 9 | 3 | no | — |
| 453 | D4 | — | 9 | 2 | no | — |
| 454 | D4 | — | 27 | 2 | no | — |
| 455 | D4 | — | 27 | 12 | no | — |
| 456 | D4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 457 | C2×C4 | — | 9 | 3 | no | — |
| 458 | C2×C4 | — | 9 | 12 | no | — |
| 459 | C2×C4 | — | 9 | 1 | no | — |
| 460 | C2×C4 | — | 9 | 3 | no | — |
| 461 | C2×C4 | — | 9 | 3 | no | — |
| 462 | C2×C4 | — | 9 | 3 | no | — |
| 463 | C2×C4 | — | 9 | 12 | no | — |
| 464 | C2×C4 | — | 27 | 6 | no | — |
| 465 | C2×C4 | — | 27 | 12 | no | — |
| 466 | C2×C4 | — | 27 | 12 | no | — |
| 467 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 468 | C2×C3 | — | 2 | 3 | no | — |
| 469 | C2×C3 | — | 3 | 2 | no | — |
| 470 | C2×C3 | — | 6 | 6 | no | — |
| 471 | C2×C3 | — | 6 | 1 | no | — |
| 472 | C2×C3 | — | 9 | 2 | no | — |
| 473 | C2×C3 | — | 12 | 3 | no | — |
| 474 | C2×C3 | — | 18 | 4 | no | — |
| 475 | C2×C3 | — | 18 | 3 | no | — |
| 476 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 477 | D3 | — | 3 | 4 | no | — |
| 478 | D3 | — | 6 | 2 | no | — |
| 479 | D3 | — | 6 | 6 | no | — |
| 480 | D3 | — | 6 | 4 | no | — |
| 481 | D3 | — | 12 | 3 | no | — |
| 482 | D3 | — | 18 | 4 | no | — |
| 483 | C22 | — | 9 | 1 | no | — |
| 484 | C22 | — | 9 | 4 | no | — |
| 485 | C22 | — | 9 | 3 | no | — |
| 486 | C22 | — | 18 | 6 | no | — |
| 487 | C22 | — | 54 | 4 | no | — |
| 488 | C22 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 489 | C4 | — | 9 | 1 | no | — |
| 490 | C4 | — | 9 | 3 | no | — |
| 491 | C4 | — | 9 | 12 | no | — |
| 492 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 493 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 494 | C3 | — | 3 | 2 | no | — |
| 495 | C3 | — | 6 | 1 | no | — |
| 496 | C3 | #10596694 | 1 | 1 | yes | characteristic |
| 497 | C2 | — | 2 | 3 | no | — |
| 498 | C2 | — | 9 | 2 | no | — |
| 499 | C2 | — | 18 | 3 | no | — |
| 500 | C2 | — | 18 | 4 | no | — |
| 501 | C2 | C23×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #41×#272 | C2 | semidirect |
| 2. #11722639 | C2 | semidirect |
| 3. Q8×((C3⋊D3)⋊C3)⋊C2 | C2 | semidirect |
| 4. #11722517 | C2 | semidirect |
| 5. #11722505 | C2 | semidirect |
| 6. #11722502 | C2 | semidirect |
| 7. #11722491 | C2 | semidirect |
| 8. C2×#88651 | C2 | semidirect |
| 9. #11722482 | C2 | semidirect |
| 11. #41×H(3,𝔽3) | C22 | semidirect |
| 12. #88748 | C22 | semidirect |
| 14. #88744 | C22 | semidirect |
| 16. #88740 | C22 | semidirect |
| 18. Q8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 19. #3830⋊C3 | C22 | semidirect |
| 20. #3828⋊C3 | C22 | semidirect |
| 21. C2×#634⋊C3 | C22 | semidirect |
| 24. #88672 | C22 | semidirect |
| 25. #88671 | C22 | semidirect |
| 26. C2×#6196 | C22 | semidirect |
| 29. #88652 | C22 | semidirect |
| 32. #88651 | C22 | semidirect |
| 33. #88651 | C22 | semidirect |
| 34. #88650 | C22 | semidirect |
| 35. #88649 | C22 | semidirect |
| 36. ((C3⋊D3)⋊C3)⋊Q8 | C22 | semidirect |
| 37. #64367 | D3 | semidirect |
| 78. C32×#41 | C2×D3 | semidirect |
| 79. Q8×C3⋊D3 | C2×D3 | semidirect |
| 80. #3830 | C2×D3 | semidirect |
| 81. #3828 | C2×D3 | semidirect |
| 82. C2×#634 | C2×D3 | semidirect |
| 200. #272 | 2−1+4 | semidirect |
| 299. H(3,𝔽3) | C2×2−1+4 | semidirect |
| 392. #41 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 441. C32 | 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×#272 | 2 |
| #11722639 | 2 |
| Q8×((C3⋊D3)⋊C3)⋊C2 | 2 |
| #11722517 | 2 |
| #11722505 | 2 |
| #11722502 | 2 |
| #11722491 | 2 |
| C2×#88651 | 2 |
| #11722482 | 2 |
| D3×#1010 | 3 |