Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 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. #5730 | C2 | semidirect |
| 3. C3×#476 | C2 | semidirect |
| 4. #5080 | C2 | semidirect |
| 5. C4×#214 | C2 | semidirect |
| 6. #4862 | C2 | semidirect |
| 7. D3×#106 | C2 | semidirect |
| 8. #4851 | C2 | semidirect |
| 9. #4834 | C2 | semidirect |
| 10. #4778 | C2 | semidirect |
| 11. #4777 | C2 | semidirect |
| 47. #476 | D3 | semidirect |
| 131. D12 | SD16 | semidirect |
| 141. C3⋊C8 | #41 | semidirect |
| 241. C3 | #3335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5730 | 2 |
| #5551 | 2 |
| C3×#476 | 2 |
| #5080 | 2 |
| C4×#214 | 2 |
| #4862 | 2 |
| D3×#106 | 2 |
| #4851 | 2 |
| #4834 | 2 |
| #4778 | 2 |
| #4777 | 2 |
| #3335 | 3 |