Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
172 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 53 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. #5092 | C2 | semidirect |
| 5. C3×#332 | C2 | semidirect |
| 6. #4482 | C2 | semidirect |
| 7. #4479 | C2 | semidirect |
| 30. #332 | D3 | semidirect |
| 75. D12 | Q16 | semidirect |
| 152. C3 | #1669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5092 | 2 |
| #5087 | 2 |
| #4846 | 2 |
| #4834 | 2 |
| C3×#332 | 2 |
| #4482 | 2 |
| #4479 | 2 |
| #1669 | 3 |