Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #5582 | C2 | semidirect |
| 2. C3×C4×Q16 | C2 | semidirect |
| 3. #5191 | C2 | semidirect |
| 4. #5188 | C2 | semidirect |
| 5. #5026 | C2 | semidirect |
| 7. #4874 | C2 | semidirect |
| 8. #4812 | C2 | semidirect |
| 9. #4794 | C2 | semidirect |
| 10. C4×D24 | C2 | semidirect |
| 11. #4689 | C2 | semidirect |
| 48. C4×Q16 | D3 | semidirect |
| 229. C3 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5582 | 2 |
| C3×C4×Q16 | 2 |
| #5191 | 2 |
| #5188 | 2 |
| #5026 | 2 |
| #4883 | 2 |
| #4874 | 2 |
| #4812 | 2 |
| #4794 | 2 |
| C4×D24 | 2 |
| #4689 | 2 |
| #3175 | 3 |