Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#14556073 | C2 | semidirect |
| 2. C2×#17986275 | C2 | semidirect |
| 4. C2×#17985811 | C2 | semidirect |
| 5. #22590059 | C2 | semidirect |
| 6. C2×#17985782 | C2 | semidirect |
| 7. C71×#1382 | C2 | semidirect |
| 40. C2×Dic284 | D4 | semidirect |
| 70. C2×C16×C71 | D4 | semidirect |
| 72. #108×C71 | D4 | semidirect |
| 201. #1382 | D71 | semidirect |
| 202. C71 | #13321 | semidirect |
| 263. C2×C16 | D284 | semidirect |
| 265. #108 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556073 | 2 |
| C2×#17986275 | 2 |
| #22597989 | 2 |
| C2×#17985811 | 2 |
| #22590059 | 2 |
| C2×#17985782 | 2 |
| C71×#1382 | 2 |
| #13321 | 71 |