Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. #5584 | C2 | semidirect |
| 2. Q8×D12 | C2 | semidirect |
| 3. C3×#446 | C2 | semidirect |
| 4. #4850 | C2 | semidirect |
| 5. #4846 | C2 | semidirect |
| 7. #4841 | C2 | semidirect |
| 8. #4714 | C2 | semidirect |
| 9. #4710 | C2 | semidirect |
| 11. #4681 | C2 | semidirect |
| 50. #446 | D3 | semidirect |
| 239. C3 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5584 | 2 |
| Q8×D12 | 2 |
| C3×#446 | 2 |
| #4850 | 2 |
| #4846 | 2 |
| #4844 | 2 |
| #4841 | 2 |
| #4714 | 2 |
| #4710 | 2 |
| C4×D24 | 2 |
| #4681 | 2 |
| #3367 | 3 |