Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#916 | C2 | semidirect |
| 2. #5577 | C2 | semidirect |
| 3. #5555 | C2 | semidirect |
| 4. C3×C4×SD16 | C2 | semidirect |
| 5. #5031 | C2 | semidirect |
| 6. #5015 | C2 | semidirect |
| 7. #4864 | C2 | semidirect |
| 8. #4808 | C2 | semidirect |
| 9. #4781 | C2 | semidirect |
| 10. #4693 | C2 | semidirect |
| 11. C8×D12 | C2 | semidirect |
| 52. C4×SD16 | D3 | semidirect |
| 72. C3×SD16 | D4 | semidirect |
| 178. SD16 | D12 | semidirect |
| 211. C3×C4 | #135 | semidirect |
| 271. C4 | #916 | semidirect |
| 274. C3 | #3284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#916 | 2 |
| #5577 | 2 |
| #5555 | 2 |
| C3×C4×SD16 | 2 |
| #5031 | 2 |
| #5015 | 2 |
| #4864 | 2 |
| #4808 | 2 |
| #4781 | 2 |
| #4693 | 2 |
| C8×D12 | 2 |
| #3284 | 3 |