Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 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. #5727 | C2 | semidirect |
| 3. C3×#461 | C2 | semidirect |
| 4. #5171 | C2 | semidirect |
| 5. #5170 | C2 | semidirect |
| 6. #5079 | C2 | semidirect |
| 7. C4×#214 | C2 | semidirect |
| 8. #4851 | C2 | semidirect |
| 9. #4834 | C2 | semidirect |
| 10. #4805 | C2 | semidirect |
| 11. D3×#103 | C2 | semidirect |
| 48. #461 | D3 | semidirect |
| 135. D12 | SD16 | semidirect |
| 143. Dic6 | #41 | semidirect |
| 251. C3 | #3298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5727 | 2 |
| #5551 | 2 |
| C3×#461 | 2 |
| #5171 | 2 |
| #5170 | 2 |
| #5079 | 2 |
| C4×#214 | 2 |
| #4851 | 2 |
| #4834 | 2 |
| #4805 | 2 |
| D3×#103 | 2 |
| #3298 | 3 |