Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
278 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 63 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. #5483 | C2 | semidirect |
| 5. C3×#342 | C2 | semidirect |
| 6. #4527 | C2 | semidirect |
| 7. #4526 | C2 | semidirect |
| 28. #342 | D3 | semidirect |
| 30. C23×D3 | Q8 | semidirect |
| 43. C22×Dic3 | Q8 | semidirect |
| 225. C3 | #2032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5483 | 2 |
| C2×#806 | 2 |
| C3×#342 | 2 |
| #4527 | 2 |
| #4526 | 2 |
| #2032 | 3 |