Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
| 2. #5576 | C2 | semidirect |
| 3. C3×C4×Q16 | C2 | semidirect |
| 4. #5028 | C2 | semidirect |
| 5. #4886 | C2 | semidirect |
| 6. #4810 | C2 | semidirect |
| 7. #4809 | C2 | semidirect |
| 8. #4696 | C2 | semidirect |
| 9. #4688 | C2 | semidirect |
| 44. C4×Q16 | D3 | semidirect |
| 60. C3×Q16 | D4 | semidirect |
| 149. Q16 | D12 | semidirect |
| 229. C3 | #3277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#918 | 2 |
| #5576 | 2 |
| C3×C4×Q16 | 2 |
| #5028 | 2 |
| #4886 | 2 |
| #4810 | 2 |
| #4809 | 2 |
| #4696 | 2 |
| #4688 | 2 |
| #3277 | 3 |