Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
400 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. C3×C4×Dic18 | C2 | semidirect |
| 4. #11720516 | C2 | semidirect |
| 6. #11720268 | C2 | semidirect |
| 7. #11720263 | C2 | semidirect |
| 21. #88423 | C4 | semidirect |
| 31. C4×Dic18 | D3 | semidirect |
| 48. C3×Dic18 | C2×C4 | semidirect |
| 50. C3⋊(C9⋊C8) | C2×C4 | semidirect |
| 134. Dic18 | C4×D3 | semidirect |
| 205. C3×C9 | #440 | semidirect |
| 291. C9 | #5026 | semidirect |
| 329. C3 | #10588694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×D12 | 2 |
| C3×C4×Dic18 | 2 |
| C2×#88423 | 2 |
| #11720516 | 2 |
| #11720294 | 2 |
| #11720268 | 2 |
| #11720263 | 2 |
| #10590358 | 3 |
| #10588694 | 3 |