Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
524 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×(C3⋊D9)⋊Q8 | C2 | semidirect |
| 2. C2×C9×#204 | C2 | semidirect |
| 4. C2×#88423 | C2 | semidirect |
| 5. #11720542 | C2 | semidirect |
| 6. C3×#63376 | C2 | semidirect |
| 7. #11720297 | C2 | semidirect |
| 39. #63376 | D3 | semidirect |
| 52. C9×Dic6 | D4 | semidirect |
| 54. C3×Dic18 | D4 | semidirect |
| 98. C2×C3⋊D9 | SD16 | semidirect |
| 114. C2×#204 | D9 | semidirect |
| 165. Dic18 | D12 | semidirect |
| 249. C3×C9 | #448 | semidirect |
| 290. Dic6 | #611 | semidirect |
| 361. C9 | #4806 | semidirect |
| 410. C3 | #10588850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C3⋊D9)⋊Q8 | 2 |
| C2×C9×#204 | 2 |
| #11721045 | 2 |
| C2×#88423 | 2 |
| #11720542 | 2 |
| C3×#63376 | 2 |
| #11720297 | 2 |
| #10590824 | 3 |
| #10588850 | 3 |