Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 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×#918 | C2 | semidirect |
| 3. Q8×D12 | C2 | semidirect |
| 4. C3×C4×Q16 | C2 | semidirect |
| 5. #5031 | C2 | semidirect |
| 6. #5027 | C2 | semidirect |
| 7. #4886 | C2 | semidirect |
| 8. #4808 | C2 | semidirect |
| 9. #4806 | C2 | semidirect |
| 10. #4693 | C2 | semidirect |
| 11. #4688 | C2 | semidirect |
| 52. C4×Q16 | D3 | semidirect |
| 71. C3×Q16 | D4 | semidirect |
| 174. Q16 | D12 | semidirect |
| 208. C3×C4 | #137 | semidirect |
| 264. C4 | #918 | semidirect |
| 267. C3 | #3278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#918 | 2 |
| #5577 | 2 |
| Q8×D12 | 2 |
| C3×C4×Q16 | 2 |
| #5031 | 2 |
| #5027 | 2 |
| #4886 | 2 |
| #4808 | 2 |
| #4806 | 2 |
| #4693 | 2 |
| #4688 | 2 |
| #3278 | 3 |