Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
792 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11724618 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3⋊D3×#208 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#63874 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11722046 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#63570 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10591009 | — | 3 | 1 | no | maximal |
| 7 | #10590392 | — | 3 | 2 | no | maximal |
| 8 | C3×#3828 | C22 | 1 | 2 | yes | — |
| 9 | C2×C3×C4×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 10 | #89049 | — | 2 | 1 | no | — |
| 11 | #89046 | — | 2 | 1 | no | — |
| 12 | C4⋊#1113 | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | C4×#1113 | — | 2 | 1 | no | — |
| 14 | #89042 | — | 2 | 1 | no | — |
| 15 | #89041 | C4 | 1 | 2 | yes | complemented |
| 16 | #89040 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #88855 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C32×C4×Dic3 | C22 | 1 | 2 | yes | complemented |
| 19 | C32×#208 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #88787 | — | 2 | 1 | no | — |
| 21 | C3⋊D3×C3⋊C8 | — | 2 | 1 | no | — |
| 22 | C3×#3724 | — | 2 | 1 | no | — |
| 23 | C3×#3722 | — | 2 | 1 | no | — |
| 24 | #64306 | — | 3 | 1 | no | — |
| 25 | D3×#235 | — | 3 | 2 | no | — |
| 26 | M16×C3⋊D3 | — | 3 | 1 | no | — |
| 27 | C3×#872 | — | 3 | 2 | no | — |
| 28 | #63874 | D3 | 1 | 1 | yes | characteristic, complemented |
| 29 | D3×#208 | — | 3 | 2 | no | — |
| 30 | D3×#208 | — | 6 | 1 | no | — |
| 31 | #63632 | — | 3 | 2 | no | — |
| 32 | C3×#825 | — | 3 | 2 | no | — |
| 33 | C3×#805 | — | 3 | 2 | no | — |
| 34 | #63570 | D3 | 1 | 2 | yes | complemented |
| 35 | #63569 | — | 3 | 2 | no | — |
| 36 | #63569 | — | 3 | 2 | no | — |
| 37 | #63569 | — | 6 | 2 | no | — |
| 38 | C22×C3×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 39 | C2×#1113 | — | 2 | 1 | no | — |
| 40 | C2×C33×C4 | C23 | 1 | 1 | yes | characteristic |
| 41 | C3×#638 | — | 2 | 2 | no | — |
| 42 | C2×C3×C3⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 43 | C3×C4⋊(C3⋊D3) | C2×C4 | 1 | 2 | yes | — |
| 44 | C3×C4×C3⋊D3 | — | 2 | 2 | no | — |
| 45 | C3×C4×C3⋊D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C3×C4×C3⋊D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | C3×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 48 | C3×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 49 | C3×#634 | C2×C4 | 1 | 2 | yes | — |
| 50 | C2×C32×Dic3 | — | 2 | 2 | no | — |
| 51 | #6296 | — | 2 | 1 | no | — |
| 52 | #6295 | — | 2 | 2 | no | — |
| 53 | #6295 | — | 2 | 1 | no | — |
| 54 | #6294 | — | 2 | 1 | no | — |
| 55 | #6294 | — | 2 | 2 | no | — |
| 56 | C3⋊(C3⋊(C3⋊C8)) | — | 2 | 1 | no | — |
| 57 | C32×C3⋊C8 | — | 2 | 1 | no | — |
| 58 | #5005 | — | 9 | 1 | no | — |
| 59 | #4821 | — | 9 | 2 | no | — |
| 60 | #3828 | C2×D3 | 1 | 2 | yes | — |
| 61 | C2×C4×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 62 | C3×#235 | — | 3 | 2 | no | — |
| 63 | C3×#235 | — | 3 | 2 | no | — |
| 64 | C3×#235 | — | 6 | 2 | no | — |
| 65 | C2×C3×C4×D3 | — | 3 | 2 | no | — |
| 66 | C2×C3×C4×D3 | — | 6 | 1 | no | — |
| 67 | #3811 | — | 6 | 1 | no | — |
| 68 | D3×#67 | — | 6 | 2 | no | — |
| 69 | #3805 | — | 6 | 1 | no | — |
| 70 | #3804 | — | 6 | 2 | no | — |
| 71 | #3802 | — | 3 | 1 | no | — |
| 72 | D3×D12 | — | 3 | 2 | no | — |
| 73 | C4×D32 | — | 6 | 2 | no | — |
| 74 | C4×D32 | — | 6 | 1 | no | — |
| 75 | #3799 | — | 3 | 2 | no | — |
| 76 | #3798 | — | 6 | 2 | no | — |
| 77 | #3798 | — | 6 | 1 | no | — |
| 78 | #3797 | — | 3 | 1 | no | — |
| 79 | #3796 | — | 3 | 2 | no | — |
| 80 | #3795 | — | 3 | 2 | no | — |
| 81 | D3×Dic6 | — | 3 | 2 | no | — |
| 82 | C32×M16 | — | 3 | 1 | no | — |
| 83 | C32×C42 | — | 3 | 2 | no | — |
| 84 | #3748 | — | 3 | 2 | no | — |
| 85 | #3748 | — | 3 | 1 | no | — |
| 86 | #3748 | — | 6 | 1 | no | — |
| 87 | #3748 | — | 6 | 2 | no | — |
| 88 | #3748 | — | 12 | 1 | no | — |
| 89 | #3743 | — | 6 | 1 | no | — |
| 90 | C8×C3⋊D3 | — | 6 | 1 | no | — |
| 91 | C3×(C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 92 | C3×Dic3⋊C4 | — | 6 | 2 | no | — |
| 93 | C3×C4×Dic3 | — | 2 | 2 | no | — |
| 94 | C3×C4×Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 95 | C3×C4×Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 96 | C3×#208 | — | 2 | 1 | no | — |
| 97 | C3×#208 | C2×D3 | 1 | 2 | yes | complemented |
| 98 | #3724 | — | 2 | 1 | no | — |
| 99 | #3722 | — | 2 | 1 | no | — |
| 100 | #3711 | — | 6 | 2 | no | — |
| 101 | #3711 | — | 6 | 2 | no | — |
| 102 | D3×C3⋊C8 | — | 6 | 2 | no | — |
| 103 | D3×C3⋊C8 | — | 6 | 2 | no | — |
| 104 | C22×C33 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 106 | C2×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 107 | C2×C3×C3⋊D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 108 | C2×C3×C3⋊D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 109 | #1113 | — | 4 | 2 | no | — |
| 110 | C33×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 111 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 113 | C3×C3⋊Dic3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 114 | C3×C3⋊Dic3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 115 | C32×Dic3 | — | 4 | 2 | no | — |
| 116 | D3×#41 | — | 9 | 2 | no | — |
| 117 | C2×#235 | — | 9 | 1 | no | — |
| 118 | C3×#117 | — | 9 | 1 | no | — |
| 119 | C2×#208 | — | 9 | 1 | no | — |
| 120 | D3×M16 | — | 9 | 2 | no | — |
| 121 | D3×M16 | — | 18 | 1 | no | — |
| 122 | #872 | — | 3 | 2 | no | — |
| 123 | C3×#104 | — | 9 | 2 | no | — |
| 124 | #837 | — | 9 | 2 | no | — |
| 125 | #825 | — | 3 | 2 | no | — |
| 126 | #805 | — | 3 | 2 | no | — |
| 127 | #805 | — | 9 | 2 | no | — |
| 128 | #805 | — | 9 | 2 | no | — |
| 129 | #805 | — | 18 | 2 | no | — |
| 130 | C22×C3⋊D3 | #67 | 1 | 1 | yes | characteristic |
| 131 | C22×C3×D3 | — | 3 | 2 | no | — |
| 132 | C22×C3×D3 | — | 6 | 1 | no | — |
| 133 | C2×D32 | — | 6 | 2 | no | — |
| 134 | C2×D32 | — | 6 | 1 | no | — |
| 135 | C2×C32×C4 | — | 2 | 1 | no | — |
| 136 | C2×C32×C4 | — | 2 | 2 | no | — |
| 137 | C2×C32×C4 | — | 4 | 1 | no | — |
| 138 | C2×C32×C4 | — | 6 | 2 | no | — |
| 139 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 140 | C2×C32×C4 | C22×D3 | 1 | 2 | yes | — |
| 141 | #638 | — | 2 | 2 | no | — |
| 142 | C2×C3⋊Dic3 | #67 | 1 | 1 | yes | characteristic |
| 143 | C4⋊(C3⋊D3) | C4×D3 | 1 | 2 | yes | — |
| 144 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 145 | C4×C3⋊D3 | C4×D3 | 1 | 1 | yes | characteristic |
| 146 | C4×C3⋊D3 | C4×D3 | 1 | 1 | yes | characteristic |
| 147 | C4×C3⋊D3 | D12 | 1 | 1 | yes | characteristic |
| 148 | C4×C3⋊D3 | D12 | 1 | 1 | yes | characteristic |
| 149 | #634 | C4×D3 | 1 | 2 | yes | — |
| 150 | C3×#67 | — | 6 | 2 | no | — |
| 151 | C3×#67 | — | 6 | 2 | no | — |
| 152 | C3×#67 | — | 12 | 2 | no | — |
| 153 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 154 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 155 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 156 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 157 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 158 | C3×D12 | — | 3 | 2 | no | — |
| 159 | C3×D12 | — | 3 | 2 | no | — |
| 160 | C3×D12 | — | 6 | 2 | no | — |
| 161 | C3×C4×D3 | — | 3 | 2 | no | — |
| 162 | C3×C4×D3 | — | 3 | 2 | no | — |
| 163 | C3×C4×D3 | — | 3 | 2 | no | — |
| 164 | C3×C4×D3 | — | 3 | 2 | no | — |
| 165 | C3×C4×D3 | — | 6 | 1 | no | — |
| 166 | C3×C4×D3 | — | 6 | 1 | no | — |
| 167 | C3×C4×D3 | — | 6 | 1 | no | — |
| 168 | C3×C4×D3 | — | 6 | 1 | no | — |
| 169 | C3×C4×D3 | — | 6 | 2 | no | — |
| 170 | C3×C4×D3 | — | 6 | 2 | no | — |
| 171 | C3×C4×D3 | — | 12 | 2 | no | — |
| 172 | C3×Dic6 | — | 3 | 2 | no | — |
| 173 | C3×Dic6 | — | 3 | 2 | no | — |
| 174 | C3×Dic6 | — | 6 | 2 | no | — |
| 175 | #627 | — | 6 | 2 | no | — |
| 176 | #627 | — | 6 | 1 | no | — |
| 177 | #626 | — | 6 | 2 | no | — |
| 178 | #626 | — | 6 | 2 | no | — |
| 179 | #626 | — | 6 | 2 | no | — |
| 180 | #625 | — | 6 | 2 | no | — |
| 181 | #625 | — | 6 | 1 | no | — |
| 182 | #624 | — | 6 | 2 | no | — |
| 183 | #624 | — | 6 | 1 | no | — |
| 184 | D3×Dic3 | — | 6 | 2 | no | — |
| 185 | D3×Dic3 | — | 6 | 2 | no | — |
| 186 | D3×Dic3 | — | 6 | 2 | no | — |
| 187 | C32×C8 | — | 6 | 1 | no | — |
| 188 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 189 | C3⋊(C3⋊C8) | — | 6 | 2 | no | — |
| 190 | C3⋊(C3⋊C8) | — | 6 | 2 | no | — |
| 191 | C3⋊(C3⋊C8) | — | 12 | 2 | no | — |
| 192 | C3⋊(C3⋊C8) | — | 12 | 2 | no | — |
| 193 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 194 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 195 | #421 | — | 27 | 1 | no | Sylow |
| 196 | C2×C33 | — | 2 | 1 | no | — |
| 197 | C2×C33 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 198 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 199 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 200 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 201 | C3×#41 | — | 9 | 2 | no | — |
| 202 | C22×C3×C4 | — | 9 | 1 | no | — |
| 203 | C2×#67 | — | 18 | 1 | no | — |
| 204 | #239 | — | 9 | 2 | no | — |
| 205 | D3×Q8 | — | 9 | 2 | no | — |
| 206 | #237 | — | 9 | 2 | no | — |
| 207 | #237 | — | 18 | 2 | no | — |
| 208 | D3×D4 | — | 9 | 2 | no | — |
| 209 | D3×D4 | — | 18 | 2 | no | — |
| 210 | #235 | — | 3 | 2 | no | — |
| 211 | #235 | — | 3 | 2 | no | — |
| 212 | #235 | — | 6 | 2 | no | — |
| 213 | #235 | — | 9 | 2 | no | — |
| 214 | #235 | — | 18 | 2 | no | — |
| 215 | #235 | — | 18 | 1 | no | — |
| 216 | #235 | — | 18 | 1 | no | — |
| 217 | C2×D12 | — | 9 | 1 | no | — |
| 218 | C2×C4×D3 | — | 3 | 2 | no | — |
| 219 | C2×C4×D3 | — | 6 | 1 | no | — |
| 220 | C2×C4×D3 | — | 18 | 2 | no | — |
| 221 | C2×C4×D3 | — | 18 | 1 | no | — |
| 222 | C2×Dic6 | — | 9 | 1 | no | — |
| 223 | C3×M16 | — | 3 | 2 | no | — |
| 224 | C3×M16 | — | 6 | 1 | no | — |
| 225 | C3×C4⋊C4 | — | 18 | 1 | no | — |
| 226 | C3×C22⋊C4 | — | 18 | 1 | no | — |
| 227 | C3×C42 | — | 3 | 2 | no | — |
| 228 | C3×C42 | — | 3 | 2 | no | — |
| 229 | C3×C42 | — | 6 | 2 | no | — |
| 230 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 231 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 232 | C4×Dic3 | D32 | 1 | 2 | yes | complemented |
| 233 | #208 | — | 9 | 1 | no | — |
| 234 | #208 | — | 9 | 2 | no | — |
| 235 | #208 | — | 18 | 1 | no | — |
| 236 | #208 | — | 18 | 2 | no | — |
| 237 | #208 | — | 18 | 1 | no | — |
| 238 | #208 | — | 36 | 1 | no | — |
| 239 | #208 | D32 | 1 | 1 | yes | characteristic, complemented |
| 240 | C2×C3⋊C8 | — | 18 | 1 | no | — |
| 241 | ΓL(1,𝔽25) | — | 18 | 2 | no | — |
| 242 | ΓL(1,𝔽25) | — | 18 | 2 | no | — |
| 243 | D3×C8 | — | 18 | 2 | no | — |
| 244 | D3×C8 | — | 18 | 2 | no | — |
| 245 | C22×C32 | — | 2 | 1 | no | — |
| 246 | C22×C32 | — | 2 | 2 | no | — |
| 247 | C22×C32 | — | 4 | 1 | no | — |
| 248 | C22×C32 | D3×D4 | 1 | 2 | yes | — |
| 249 | C22×C32 | C2×#67 | 1 | 1 | yes | characteristic |
| 250 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 251 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 252 | C2×C3⋊D3 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 253 | C2×C3⋊D3 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 254 | C2×C3×D3 | — | 3 | 2 | no | — |
| 255 | C2×C3×D3 | — | 3 | 2 | no | — |
| 256 | C2×C3×D3 | — | 6 | 1 | no | — |
| 257 | C2×C3×D3 | — | 6 | 1 | no | — |
| 258 | C2×C3×D3 | — | 6 | 2 | no | — |
| 259 | C2×C3×D3 | — | 6 | 2 | no | — |
| 260 | C2×C3×D3 | — | 12 | 2 | no | — |
| 261 | C2×C3×D3 | — | 12 | 2 | no | — |
| 262 | C2×C3×D3 | — | 12 | 2 | no | — |
| 263 | D32 | — | 12 | 4 | no | — |
| 264 | D32 | — | 12 | 2 | no | — |
| 265 | C32×C4 | — | 2 | 2 | no | — |
| 266 | C32×C4 | — | 2 | 1 | no | — |
| 267 | C32×C4 | — | 2 | 2 | no | — |
| 268 | C32×C4 | — | 2 | 1 | no | — |
| 269 | C32×C4 | — | 4 | 1 | no | — |
| 270 | C32×C4 | — | 4 | 1 | no | — |
| 271 | C32×C4 | — | 12 | 2 | no | — |
| 272 | C32×C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 273 | C32×C4 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 274 | C32×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 275 | C32×C4 | D3×D4 | 1 | 2 | yes | — |
| 276 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 277 | C3⋊Dic3 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 278 | C3⋊Dic3 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 279 | C3×Dic3 | — | 3 | 2 | no | — |
| 280 | C3×Dic3 | — | 3 | 2 | no | — |
| 281 | C3×Dic3 | — | 4 | 2 | no | — |
| 282 | C3×Dic3 | — | 4 | 2 | no | — |
| 283 | C3×Dic3 | — | 4 | 4 | no | — |
| 284 | C3×Dic3 | — | 6 | 1 | no | — |
| 285 | C3×Dic3 | — | 6 | 1 | no | — |
| 286 | C3×Dic3 | — | 6 | 2 | no | — |
| 287 | C3×Dic3 | — | 6 | 2 | no | — |
| 288 | C3×Dic3 | — | 12 | 2 | no | — |
| 289 | C2×#41 | — | 27 | 1 | no | — |
| 290 | C2×M16 | — | 27 | 1 | no | — |
| 291 | #117 | — | 9 | 1 | no | — |
| 292 | #104 | — | 9 | 2 | no | — |
| 293 | #104 | — | 27 | 2 | no | — |
| 294 | C33 | #421 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 295 | C23×C3 | — | 9 | 1 | no | — |
| 296 | C22×D3 | — | 3 | 2 | no | — |
| 297 | C22×D3 | — | 6 | 1 | no | — |
| 298 | C22×D3 | — | 18 | 2 | no | — |
| 299 | C22×D3 | — | 18 | 1 | no | — |
| 300 | C3×Q8 | — | 9 | 2 | no | — |
| 301 | C3×D4 | — | 9 | 2 | no | — |
| 302 | C3×D4 | — | 18 | 2 | no | — |
| 303 | C2×C3×C4 | — | 2 | 2 | no | — |
| 304 | C2×C3×C4 | — | 2 | 1 | no | — |
| 305 | C2×C3×C4 | — | 4 | 1 | no | — |
| 306 | C2×C3×C4 | — | 6 | 2 | no | — |
| 307 | C2×C3×C4 | — | 6 | 2 | no | — |
| 308 | C2×C3×C4 | — | 9 | 1 | no | — |
| 309 | C2×C3×C4 | — | 9 | 1 | no | — |
| 310 | C2×C3×C4 | — | 9 | 1 | no | — |
| 311 | C2×C3×C4 | — | 9 | 1 | no | — |
| 312 | C2×C3×C4 | — | 9 | 1 | no | — |
| 313 | C2×C3×C4 | — | 12 | 2 | no | — |
| 314 | C2×C3×C4 | — | 18 | 2 | no | — |
| 315 | C2×C3×C4 | C2×D32 | 1 | 2 | yes | — |
| 316 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 317 | #67 | — | 6 | 2 | no | — |
| 318 | #67 | — | 6 | 2 | no | — |
| 319 | #67 | — | 12 | 2 | no | — |
| 320 | #67 | — | 18 | 2 | no | — |
| 321 | #67 | — | 18 | 2 | no | — |
| 322 | #67 | — | 18 | 2 | no | — |
| 323 | C2×Dic3 | — | 2 | 2 | no | — |
| 324 | C2×Dic3 | — | 3 | 2 | no | — |
| 325 | C2×Dic3 | — | 6 | 1 | no | — |
| 326 | C2×Dic3 | — | 18 | 2 | no | — |
| 327 | C2×Dic3 | — | 18 | 1 | no | — |
| 328 | D12 | — | 3 | 2 | no | — |
| 329 | D12 | — | 3 | 2 | no | — |
| 330 | D12 | — | 6 | 2 | no | — |
| 331 | D12 | — | 18 | 1 | no | — |
| 332 | D12 | — | 18 | 2 | no | — |
| 333 | C4×D3 | — | 3 | 2 | no | — |
| 334 | C4×D3 | — | 3 | 2 | no | — |
| 335 | C4×D3 | — | 3 | 2 | no | — |
| 336 | C4×D3 | — | 3 | 2 | no | — |
| 337 | C4×D3 | — | 6 | 1 | no | — |
| 338 | C4×D3 | — | 6 | 1 | no | — |
| 339 | C4×D3 | — | 6 | 1 | no | — |
| 340 | C4×D3 | — | 6 | 1 | no | — |
| 341 | C4×D3 | — | 6 | 2 | no | — |
| 342 | C4×D3 | — | 6 | 2 | no | — |
| 343 | C4×D3 | — | 12 | 2 | no | — |
| 344 | C4×D3 | — | 18 | 2 | no | — |
| 345 | C4×D3 | — | 18 | 2 | no | — |
| 346 | C4×D3 | — | 18 | 2 | no | — |
| 347 | Dic6 | — | 3 | 2 | no | — |
| 348 | Dic6 | — | 3 | 2 | no | — |
| 349 | Dic6 | — | 6 | 2 | no | — |
| 350 | Dic6 | — | 18 | 2 | no | — |
| 351 | Dic6 | — | 18 | 1 | no | — |
| 352 | C3×C8 | — | 6 | 2 | no | — |
| 353 | C3×C8 | — | 6 | 2 | no | — |
| 354 | C3⋊C8 | — | 2 | 1 | no | — |
| 355 | C3⋊C8 | — | 18 | 2 | no | — |
| 356 | C3⋊C8 | — | 18 | 2 | no | — |
| 357 | C3⋊C8 | — | 18 | 1 | no | — |
| 358 | C3⋊C8 | — | 36 | 2 | no | — |
| 359 | C3⋊C8 | — | 36 | 2 | no | — |
| 360 | C2×C32 | — | 2 | 1 | no | — |
| 361 | C2×C32 | — | 2 | 2 | no | — |
| 362 | C2×C32 | — | 2 | 2 | no | — |
| 363 | C2×C32 | — | 2 | 1 | no | — |
| 364 | C2×C32 | — | 4 | 1 | no | — |
| 365 | C2×C32 | — | 4 | 2 | no | — |
| 366 | C2×C32 | — | 4 | 1 | no | — |
| 367 | C2×C32 | — | 8 | 1 | no | — |
| 368 | C2×C32 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 369 | C2×C32 | C2×(C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 370 | C3⋊D3 | — | 2 | 1 | no | — |
| 371 | C3⋊D3 | — | 2 | 1 | no | — |
| 372 | C3⋊D3 | — | 4 | 2 | no | — |
| 373 | C3×D3 | — | 6 | 2 | no | — |
| 374 | C3×D3 | — | 6 | 2 | no | — |
| 375 | C3×D3 | — | 6 | 2 | no | — |
| 376 | C3×D3 | — | 12 | 1 | no | — |
| 377 | C3×D3 | — | 12 | 2 | no | — |
| 378 | C3×D3 | — | 12 | 2 | no | — |
| 379 | C3×D3 | — | 24 | 2 | no | — |
| 380 | #41 | — | 9 | 2 | no | — |
| 381 | #41 | — | 27 | 2 | no | — |
| 382 | #41 | — | 54 | 1 | no | — |
| 383 | #41 | — | 54 | 1 | no | — |
| 384 | C2×Q8 | — | 27 | 1 | no | — |
| 385 | C2×D4 | — | 27 | 1 | no | — |
| 386 | C2×D4 | — | 54 | 1 | no | — |
| 387 | C22×C4 | — | 9 | 1 | no | — |
| 388 | C22×C4 | — | 54 | 1 | no | — |
| 389 | M16 | — | 3 | 1 | no | — |
| 390 | M16 | — | 27 | 1 | no | — |
| 391 | M16 | — | 54 | 1 | no | — |
| 392 | C2×C8 | — | 54 | 1 | no | — |
| 393 | C4⋊C4 | — | 18 | 1 | no | — |
| 394 | C22⋊C4 | — | 18 | 1 | no | — |
| 395 | C42 | — | 3 | 2 | no | — |
| 396 | C22×C3 | — | 2 | 1 | no | — |
| 397 | C22×C3 | — | 2 | 2 | no | — |
| 398 | C22×C3 | — | 4 | 1 | no | — |
| 399 | C22×C3 | — | 9 | 1 | no | — |
| 400 | C22×C3 | — | 9 | 1 | no | — |
| 401 | C22×C3 | — | 18 | 2 | no | — |
| 402 | C22×C3 | — | 36 | 1 | no | — |
| 403 | C22×C3 | #3802 | 1 | 1 | yes | characteristic |
| 404 | C22×C3 | D3×#67 | 1 | 2 | yes | — |
| 405 | C2×D3 | — | 3 | 2 | no | — |
| 406 | C2×D3 | — | 3 | 2 | no | — |
| 407 | C2×D3 | — | 6 | 1 | no | — |
| 408 | C2×D3 | — | 6 | 1 | no | — |
| 409 | C2×D3 | — | 6 | 2 | no | — |
| 410 | C2×D3 | — | 6 | 2 | no | — |
| 411 | C2×D3 | — | 12 | 2 | no | — |
| 412 | C2×D3 | — | 12 | 2 | no | — |
| 413 | C2×D3 | — | 12 | 2 | no | — |
| 414 | C2×D3 | — | 36 | 4 | no | — |
| 415 | C2×D3 | — | 36 | 2 | no | — |
| 416 | C3×C4 | — | 2 | 2 | no | — |
| 417 | C3×C4 | — | 2 | 1 | no | — |
| 418 | C3×C4 | — | 2 | 1 | no | — |
| 419 | C3×C4 | — | 2 | 2 | no | — |
| 420 | C3×C4 | — | 4 | 1 | no | — |
| 421 | C3×C4 | — | 4 | 1 | no | — |
| 422 | C3×C4 | — | 9 | 1 | no | — |
| 423 | C3×C4 | — | 9 | 1 | no | — |
| 424 | C3×C4 | — | 12 | 2 | no | — |
| 425 | C3×C4 | — | 12 | 2 | no | — |
| 426 | C3×C4 | — | 12 | 4 | no | — |
| 427 | C3×C4 | — | 18 | 2 | no | — |
| 428 | C3×C4 | C4×D32 | 1 | 2 | yes | — |
| 429 | C3×C4 | C4×D32 | 1 | 1 | yes | characteristic |
| 430 | C3×C4 | D3×D12 | 1 | 2 | yes | — |
| 431 | C3×C4 | #3811 | 1 | 1 | yes | characteristic |
| 432 | Dic3 | — | 3 | 2 | no | — |
| 433 | Dic3 | — | 3 | 2 | no | — |
| 434 | Dic3 | — | 4 | 2 | no | — |
| 435 | Dic3 | — | 6 | 1 | no | — |
| 436 | Dic3 | — | 6 | 1 | no | — |
| 437 | Dic3 | — | 6 | 2 | no | — |
| 438 | Dic3 | — | 6 | 2 | no | — |
| 439 | Dic3 | — | 12 | 2 | no | — |
| 440 | C32 | — | 2 | 1 | no | — |
| 441 | C32 | — | 2 | 2 | no | — |
| 442 | C32 | — | 4 | 1 | no | — |
| 443 | C32 | #4821 | 1 | 2 | yes | complemented |
| 444 | C32 | #5005 | 1 | 1 | yes | characteristic, complemented |
| 445 | C23 | — | 9 | 1 | no | — |
| 446 | C23 | — | 54 | 1 | no | — |
| 447 | Q8 | — | 9 | 2 | no | — |
| 448 | Q8 | — | 54 | 1 | no | — |
| 449 | D4 | — | 9 | 2 | no | — |
| 450 | D4 | — | 18 | 2 | no | — |
| 451 | D4 | — | 54 | 1 | no | — |
| 452 | D4 | — | 54 | 2 | no | — |
| 453 | C2×C4 | — | 6 | 2 | no | — |
| 454 | C2×C4 | — | 9 | 1 | no | — |
| 455 | C2×C4 | — | 9 | 1 | no | — |
| 456 | C2×C4 | — | 9 | 1 | no | — |
| 457 | C2×C4 | — | 9 | 1 | no | — |
| 458 | C2×C4 | — | 9 | 1 | no | — |
| 459 | C2×C4 | — | 18 | 2 | no | — |
| 460 | C2×C4 | — | 54 | 2 | no | — |
| 461 | C2×C4 | — | 54 | 1 | no | — |
| 462 | C2×C4 | D33 | 1 | 1 | yes | characteristic |
| 463 | C8 | — | 6 | 1 | no | — |
| 464 | C8 | — | 54 | 1 | no | — |
| 465 | C2×C3 | — | 2 | 1 | no | — |
| 466 | C2×C3 | — | 2 | 2 | no | — |
| 467 | C2×C3 | — | 2 | 1 | no | — |
| 468 | C2×C3 | — | 2 | 2 | no | — |
| 469 | C2×C3 | — | 4 | 2 | no | — |
| 470 | C2×C3 | — | 4 | 1 | no | — |
| 471 | C2×C3 | — | 4 | 1 | no | — |
| 472 | C2×C3 | — | 8 | 1 | no | — |
| 473 | C2×C3 | — | 18 | 1 | no | — |
| 474 | C2×C3 | — | 18 | 1 | no | — |
| 475 | C2×C3 | — | 36 | 2 | no | — |
| 476 | C2×C3 | D3×(C2×D3)⋊C4 | 1 | 2 | yes | — |
| 477 | C2×C3 | #63921 | 1 | 1 | yes | characteristic |
| 478 | D3 | — | 6 | 2 | no | — |
| 479 | D3 | — | 6 | 2 | no | — |
| 480 | D3 | — | 6 | 2 | no | — |
| 481 | D3 | — | 12 | 1 | no | — |
| 482 | D3 | — | 12 | 2 | no | — |
| 483 | D3 | — | 12 | 2 | no | — |
| 484 | D3 | — | 24 | 2 | no | — |
| 485 | C22 | — | 9 | 1 | no | — |
| 486 | C22 | — | 9 | 1 | no | — |
| 487 | C22 | — | 18 | 2 | no | — |
| 488 | C22 | — | 36 | 1 | no | — |
| 489 | C22 | — | 108 | 2 | no | — |
| 490 | C22 | #88953 | 1 | 1 | yes | characteristic |
| 491 | C4 | — | 9 | 1 | no | — |
| 492 | C4 | — | 9 | 1 | no | — |
| 493 | C4 | — | 12 | 2 | no | — |
| 494 | C4 | — | 18 | 2 | no | — |
| 495 | C4 | #88949 | 1 | 1 | yes | characteristic |
| 496 | C4 | #88955 | 1 | 1 | yes | characteristic |
| 497 | C3 | — | 2 | 1 | no | — |
| 498 | C3 | — | 2 | 2 | no | — |
| 499 | C3 | — | 4 | 1 | no | — |
| 500 | C3 | #10590392 | 1 | 2 | yes | complemented |
| 501 | C3 | #10591009 | 1 | 1 | yes | characteristic, complemented |
| 502 | C2 | — | 2 | 1 | no | — |
| 503 | C2 | — | 18 | 1 | no | — |
| 504 | C2 | — | 18 | 1 | no | — |
| 505 | C2 | — | 36 | 2 | no | — |
| 506 | C2 | #11722905 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊D3×#208 | C2 | semidirect |
| 3. C3×#63874 | C2 | semidirect |
| 4. #11722046 | C2 | semidirect |
| 5. C3×#63570 | C2 | semidirect |
| 12. C4⋊#1113 | C4 | semidirect |
| 15. #89041 | C4 | semidirect |
| 16. #89040 | C4 | semidirect |
| 17. #88855 | C22 | semidirect |
| 18. C32×C4×Dic3 | C22 | semidirect |
| 19. C32×#208 | C22 | semidirect |
| 28. #63874 | D3 | semidirect |
| 34. #63570 | D3 | semidirect |
| 94. C3×C4×Dic3 | C2×D3 | semidirect |
| 95. C3×C4×Dic3 | C2×D3 | semidirect |
| 97. C3×#208 | C2×D3 | semidirect |
| 232. C4×Dic3 | D32 | semidirect |
| 239. #208 | D32 | semidirect |
| 294. C33 | #421 | semidirect |
| 443. C32 | #4821 | semidirect |
| 444. C32 | #5005 | semidirect |
| 500. C3 | #10590392 | semidirect |
| 501. C3 | #10591009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724618 | 2 |
| C3⋊D3×#208 | 2 |
| C3×#63874 | 2 |
| #11722046 | 2 |
| C3×#63570 | 2 |
| #10591009 | 3 |
| #10590392 | 3 |