Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
402 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 117 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. C3×Q8×Dic9 | C2 | semidirect |
| 4. #11720582 | C2 | semidirect |
| 6. #11720279 | C2 | semidirect |
| 7. #11720274 | C2 | semidirect |
| 15. C9×#215 | C4 | semidirect |
| 30. Q8×Dic9 | D3 | semidirect |
| 39. C3×Q8×C9 | C2×C4 | semidirect |
| 50. C9×C3⋊C8 | C2×C4 | semidirect |
| 124. Q8×C9 | C4×D3 | semidirect |
| 159. #215 | Dic9 | semidirect |
| 206. C3×C9 | #440 | semidirect |
| 213. C3×Q8 | C2×Dic9 | semidirect |
| 240. C3⋊C8 | C2×Dic9 | semidirect |
| 293. C9 | #5026 | semidirect |
| 296. Q8 | D3×Dic9 | semidirect |
| 331. C3 | #10588844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×Dic9 | 2 |
| C2×C9×#215 | 2 |
| D12×Dic9 | 2 |
| #11720582 | 2 |
| #11720294 | 2 |
| #11720279 | 2 |
| #11720274 | 2 |
| #10591566 | 3 |
| #10588844 | 3 |