Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
820 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 152 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 | C2×#11718239 | C2 | 1 | 3 | yes | maximal |
| 2 | C2×#11718239 | C2 | 1 | 3 | yes | maximal |
| 3 | #13128238 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C22×#6122 | C22 | 1 | 3 | yes | — |
| 5 | C22×#6122 | C22 | 1 | 1 | yes | characteristic |
| 6 | C13×#543 | C4 | 1 | 1 | yes | characteristic |
| 7 | #11719328 | — | 2 | 6 | no | — |
| 8 | #11719327 | — | 2 | 6 | no | — |
| 9 | #11719188 | C4 | 1 | 3 | yes | — |
| 10 | C2×#88131 | C22 | 1 | 3 | yes | — |
| 11 | #11718239 | — | 2 | 6 | no | — |
| 12 | #11718239 | — | 2 | 6 | no | — |
| 13 | C23×Dic13 | C23 | 1 | 1 | yes | characteristic |
| 14 | C2×#6122 | — | 2 | 3 | no | — |
| 15 | C2×#6122 | — | 2 | 3 | no | — |
| 16 | C2×#6122 | — | 2 | 3 | no | — |
| 17 | C2×#6122 | — | 2 | 3 | no | — |
| 18 | C2×#6122 | — | 2 | 3 | no | — |
| 19 | C2×#6122 | — | 2 | 3 | no | — |
| 20 | C2×#6122 | — | 2 | 3 | no | — |
| 21 | C2×#6122 | Q8 | 1 | 6 | yes | complemented |
| 22 | C22×#1057 | — | 2 | 3 | no | — |
| 23 | C22×#1057 | Q8 | 1 | 2 | yes | complemented |
| 24 | C13×C22⋊Q8 | — | 2 | 6 | no | — |
| 25 | C2×C13×C22⋊C4 | C2×C4 | 1 | 3 | yes | — |
| 26 | C2×C22⋊Dic13 | C2×C4 | 1 | 3 | yes | — |
| 27 | Q8×Dic13 | — | 2 | 2 | no | — |
| 28 | #88198 | — | 2 | 6 | no | — |
| 29 | #88178 | — | 2 | 6 | no | — |
| 30 | C2×#6101 | — | 2 | 3 | no | — |
| 31 | C2×C4×Dic13 | — | 2 | 3 | no | — |
| 32 | #88143 | — | 2 | 12 | no | — |
| 33 | #88142 | — | 2 | 6 | no | — |
| 34 | #88141 | — | 2 | 6 | no | — |
| 35 | #88132 | — | 2 | 6 | no | — |
| 36 | #88132 | — | 2 | 6 | no | — |
| 37 | #88131 | — | 2 | 3 | no | — |
| 38 | #88131 | — | 2 | 3 | no | — |
| 39 | #88131 | D4 | 1 | 6 | yes | — |
| 40 | #88131 | D4 | 1 | 6 | yes | — |
| 41 | #11395 | — | 13 | 1 | no | maximal, Sylow |
| 42 | C24×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 43 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 44 | C22×C4×C13 | — | 2 | 3 | no | — |
| 45 | C22×Dic13 | — | 2 | 3 | no | — |
| 46 | C22×Dic13 | C2×D4 | 1 | 3 | yes | — |
| 47 | C22×Dic13 | C2×D4 | 1 | 3 | yes | — |
| 48 | C22×Dic13 | C2×Q8 | 1 | 1 | yes | characteristic |
| 49 | C22×Dic13 | C2×Q8 | 1 | 3 | yes | — |
| 50 | C22×Dic13 | #41 | 1 | 3 | yes | — |
| 51 | C22×Dic13 | #41 | 1 | 1 | yes | characteristic |
| 52 | C2×Dic26 | — | 2 | 6 | no | — |
| 53 | #6122 | — | 2 | 6 | no | — |
| 54 | #6122 | — | 2 | 6 | no | — |
| 55 | #6122 | — | 4 | 1 | no | — |
| 56 | #6122 | — | 4 | 3 | no | — |
| 57 | #6122 | — | 4 | 3 | no | — |
| 58 | #6122 | — | 4 | 3 | no | — |
| 59 | C2×#1057 | — | 2 | 6 | no | — |
| 60 | C2×#1057 | — | 2 | 6 | no | — |
| 61 | C2×#1057 | — | 4 | 3 | no | — |
| 62 | C2×#1057 | — | 4 | 3 | no | — |
| 63 | C13×C4⋊C4 | — | 2 | 6 | no | — |
| 64 | C13×C22⋊C4 | — | 2 | 3 | no | — |
| 65 | C13×C22⋊C4 | C22⋊C4 | 1 | 6 | yes | — |
| 66 | C22⋊Dic13 | — | 2 | 3 | no | — |
| 67 | C22⋊Dic13 | C22⋊C4 | 1 | 6 | yes | — |
| 68 | C4⋊Dic13 | — | 2 | 6 | no | — |
| 69 | #6101 | — | 2 | 12 | no | — |
| 70 | #6101 | — | 2 | 6 | no | — |
| 71 | #6101 | — | 2 | 6 | no | — |
| 72 | C4×Dic13 | — | 2 | 6 | no | — |
| 73 | C4×Dic13 | — | 2 | 6 | no | — |
| 74 | #3458 | — | 13 | 1 | no | — |
| 75 | C2×#344 | — | 13 | 3 | no | — |
| 76 | C2×#344 | — | 13 | 3 | no | — |
| 77 | C23×C13 | — | 8 | 1 | no | — |
| 78 | C23×C13 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 79 | C23×C13 | C4×Q8 | 1 | 1 | yes | characteristic |
| 80 | C23×C13 | C4×Q8 | 1 | 3 | yes | — |
| 81 | Q8×C13 | — | 8 | 2 | no | — |
| 82 | C2×C4×C13 | — | 2 | 6 | no | — |
| 83 | C2×C4×C13 | — | 8 | 3 | no | — |
| 84 | C2×Dic13 | — | 2 | 6 | no | — |
| 85 | C2×Dic13 | — | 8 | 3 | no | — |
| 86 | C2×Dic13 | #120 | 1 | 1 | yes | characteristic |
| 87 | C2×Dic13 | #120 | 1 | 3 | yes | — |
| 88 | C2×Dic13 | C22⋊Q8 | 1 | 3 | yes | — |
| 89 | C2×Dic13 | C22⋊Q8 | 1 | 3 | yes | — |
| 90 | C2×Dic13 | C22⋊Q8 | 1 | 3 | yes | — |
| 91 | C2×Dic13 | C22⋊Q8 | 1 | 3 | yes | — |
| 92 | C2×Dic13 | #124 | 1 | 3 | yes | — |
| 93 | C2×Dic13 | #124 | 1 | 3 | yes | — |
| 94 | C2×Dic13 | C4⋊Q8 | 1 | 3 | yes | — |
| 95 | C2×Dic13 | C4⋊Q8 | 1 | 3 | yes | — |
| 96 | Dic26 | — | 8 | 6 | no | — |
| 97 | #1057 | — | 4 | 2 | no | — |
| 98 | #1057 | — | 4 | 6 | no | — |
| 99 | C22×M16 | — | 13 | 1 | no | — |
| 100 | C22×M16 | — | 13 | 3 | no | — |
| 101 | #544 | — | 26 | 6 | no | — |
| 102 | #543 | — | 13 | 3 | no | — |
| 103 | #543 | #261 | 1 | 1 | yes | characteristic |
| 104 | #533 | — | 26 | 6 | no | — |
| 105 | C2×#117 | — | 13 | 3 | no | — |
| 106 | #344 | — | 26 | 6 | no | — |
| 107 | #344 | — | 26 | 6 | no | — |
| 108 | C22×C13 | — | 4 | 3 | no | — |
| 109 | C22×C13 | — | 4 | 1 | no | — |
| 110 | C22×C13 | — | 4 | 3 | no | — |
| 111 | C22×C13 | #379 | 1 | 1 | yes | characteristic |
| 112 | C22×C13 | #391 | 1 | 3 | yes | — |
| 113 | C22×C13 | #391 | 1 | 3 | yes | — |
| 114 | C4×C13 | — | 4 | 6 | no | — |
| 115 | Dic13 | — | 4 | 6 | no | — |
| 116 | Dic13 | #393 | 1 | 1 | yes | characteristic |
| 117 | Dic13 | #393 | 1 | 3 | yes | — |
| 118 | Dic13 | #395 | 1 | 1 | yes | characteristic |
| 119 | Dic13 | #395 | 1 | 3 | yes | — |
| 120 | C23×C4 | — | 13 | 1 | no | — |
| 121 | C2×M16 | — | 13 | 6 | no | — |
| 122 | C2×M16 | — | 26 | 3 | no | — |
| 123 | C2×M16 | — | 26 | 3 | no | — |
| 124 | C2×M16 | — | 26 | 3 | no | — |
| 125 | C2×M16 | — | 26 | 3 | no | — |
| 126 | C2×M16 | — | 26 | 3 | no | — |
| 127 | C2×M16 | — | 26 | 3 | no | — |
| 128 | C2×M16 | — | 26 | 3 | no | — |
| 129 | C22×C8 | — | 13 | 2 | no | — |
| 130 | C22×C8 | — | 26 | 3 | no | — |
| 131 | C4⋊Q8 | — | 26 | 6 | no | — |
| 132 | C4⋊Q8 | — | 26 | 6 | no | — |
| 133 | #125 | — | 26 | 12 | no | — |
| 134 | C22⋊Q8 | — | 2 | 6 | no | — |
| 135 | C22⋊Q8 | — | 26 | 6 | no | — |
| 136 | C22⋊Q8 | — | 26 | 6 | no | — |
| 137 | C22⋊Q8 | — | 26 | 6 | no | — |
| 138 | C4×Q8 | — | 26 | 6 | no | — |
| 139 | C4×Q8 | — | 26 | 2 | no | — |
| 140 | #117 | — | 13 | 6 | no | — |
| 141 | #117 | — | 13 | 6 | no | — |
| 142 | #117 | — | 26 | 3 | no | — |
| 143 | #117 | — | 26 | 3 | no | — |
| 144 | C2×C4⋊C4 | — | 26 | 3 | no | — |
| 145 | C2×C22⋊C4 | — | 13 | 3 | no | — |
| 146 | C2×C22⋊C4 | C2×#261 | 1 | 3 | yes | — |
| 147 | C2×C42 | — | 26 | 3 | no | — |
| 148 | C2×C13 | — | 2 | 1 | no | — |
| 149 | C2×C13 | — | 2 | 3 | no | — |
| 150 | C2×C13 | — | 2 | 3 | no | — |
| 151 | C2×C13 | #1446 | 1 | 1 | yes | characteristic |
| 152 | C24 | C22×#261 | 1 | 1 | yes | characteristic |
| 153 | C2×Q8 | — | 2 | 2 | no | — |
| 154 | C2×Q8 | — | 26 | 6 | no | — |
| 155 | C22×C4 | — | 2 | 3 | no | — |
| 156 | C22×C4 | — | 13 | 1 | no | — |
| 157 | C22×C4 | — | 13 | 3 | no | — |
| 158 | C22×C4 | — | 13 | 3 | no | — |
| 159 | C22×C4 | — | 13 | 1 | no | — |
| 160 | C22×C4 | — | 13 | 3 | no | — |
| 161 | C22×C4 | — | 13 | 3 | no | — |
| 162 | C22×C4 | — | 26 | 3 | no | — |
| 163 | M16 | — | 26 | 6 | no | — |
| 164 | M16 | — | 26 | 6 | no | — |
| 165 | M16 | — | 52 | 1 | no | — |
| 166 | M16 | — | 52 | 3 | no | — |
| 167 | M16 | — | 52 | 3 | no | — |
| 168 | M16 | — | 52 | 3 | no | — |
| 169 | C2×C8 | — | 26 | 6 | no | — |
| 170 | C2×C8 | — | 26 | 6 | no | — |
| 171 | C2×C8 | — | 52 | 3 | no | — |
| 172 | C2×C8 | — | 52 | 3 | no | — |
| 173 | C4⋊C4 | — | 2 | 6 | no | — |
| 174 | C4⋊C4 | — | 26 | 6 | no | — |
| 175 | C4⋊C4 | — | 26 | 6 | no | — |
| 176 | C4⋊C4 | — | 26 | 12 | no | — |
| 177 | C4⋊C4 | — | 26 | 6 | no | — |
| 178 | C22⋊C4 | — | 2 | 3 | no | — |
| 179 | C22⋊C4 | — | 13 | 6 | no | — |
| 180 | C22⋊C4 | — | 26 | 3 | no | — |
| 181 | C22⋊C4 | C22⋊#261 | 1 | 6 | yes | — |
| 182 | C42 | — | 26 | 6 | no | — |
| 183 | C42 | — | 26 | 6 | no | — |
| 184 | C13 | #11395 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 185 | C23 | — | 8 | 1 | no | — |
| 186 | C23 | Q8×#261 | 1 | 1 | yes | characteristic |
| 187 | C23 | Q8×#261 | 1 | 3 | yes | — |
| 188 | C23 | C2×C22⋊#261 | 1 | 3 | yes | — |
| 189 | Q8 | — | 8 | 2 | no | — |
| 190 | Q8 | — | 104 | 6 | no | — |
| 191 | C2×C4 | — | 2 | 6 | no | — |
| 192 | C2×C4 | — | 8 | 3 | no | — |
| 193 | C2×C4 | — | 13 | 1 | no | — |
| 194 | C2×C4 | — | 13 | 3 | no | — |
| 195 | C2×C4 | — | 13 | 3 | no | — |
| 196 | C2×C4 | — | 13 | 3 | no | — |
| 197 | C2×C4 | — | 13 | 3 | no | — |
| 198 | C2×C4 | — | 13 | 3 | no | — |
| 199 | C2×C4 | — | 13 | 3 | no | — |
| 200 | C2×C4 | — | 13 | 3 | no | — |
| 201 | C2×C4 | — | 13 | 3 | no | — |
| 202 | C2×C4 | — | 13 | 3 | no | — |
| 203 | C2×C4 | — | 26 | 6 | no | — |
| 204 | C2×C4 | — | 104 | 3 | no | — |
| 205 | C8 | — | 52 | 2 | no | — |
| 206 | C8 | — | 52 | 6 | no | — |
| 207 | C22 | — | 4 | 3 | no | — |
| 208 | C22 | — | 4 | 1 | no | — |
| 209 | C22 | — | 4 | 3 | no | — |
| 210 | C22 | (C2×#261)⋊Q8 | 1 | 3 | yes | — |
| 211 | C22 | (C2×#261)⋊Q8 | 1 | 3 | yes | — |
| 212 | C22 | #11719171 | 1 | 1 | yes | characteristic |
| 213 | C4 | — | 4 | 6 | no | — |
| 214 | C4 | — | 13 | 1 | no | — |
| 215 | C4 | — | 13 | 3 | no | — |
| 216 | C4 | — | 13 | 1 | no | — |
| 217 | C4 | — | 13 | 3 | no | — |
| 218 | C4 | — | 52 | 6 | no | — |
| 219 | C2 | — | 2 | 1 | no | — |
| 220 | C2 | — | 2 | 3 | no | — |
| 221 | C2 | — | 2 | 3 | no | — |
| 222 | C2 | #13130026 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 21. C2×#6122 | Q8 | semidirect |
| 23. C22×#1057 | Q8 | semidirect |
| 184. C13 | #11395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718239 | 2 |
| #13128238 | 2 |
| #11395 | 13 |