Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 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. #5563 | C2 | semidirect |
| 2. #5551 | C2 | semidirect |
| 3. C3×C8×D4 | C2 | semidirect |
| 4. #5114 | C2 | semidirect |
| 5. #5113 | C2 | semidirect |
| 6. #4842 | C2 | semidirect |
| 7. #4841 | C2 | semidirect |
| 8. #4734 | C2 | semidirect |
| 9. #4723 | C2 | semidirect |
| 10. C4×D24 | C2 | semidirect |
| 11. #4681 | C2 | semidirect |
| 51. C8×D4 | D3 | semidirect |
| 254. C3 | #3303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5563 | 2 |
| #5551 | 2 |
| C3×C8×D4 | 2 |
| #5114 | 2 |
| #5113 | 2 |
| #4842 | 2 |
| #4841 | 2 |
| #4734 | 2 |
| #4723 | 2 |
| C4×D24 | 2 |
| #4681 | 2 |
| #3303 | 3 |