Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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. #5728 | C2 | semidirect |
| 3. C3×#462 | C2 | semidirect |
| 5. Dic3×Q16 | C2 | semidirect |
| 6. #5083 | C2 | semidirect |
| 7. #5020 | C2 | semidirect |
| 8. #4846 | C2 | semidirect |
| 9. #4833 | C2 | semidirect |
| 10. #4814 | C2 | semidirect |
| 11. #4788 | C2 | semidirect |
| 49. #462 | D3 | semidirect |
| 267. C3 | #3107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| C4×#239 | 2 |
| C3×#462 | 2 |
| #5187 | 2 |
| Dic3×Q16 | 2 |
| #5083 | 2 |
| #5020 | 2 |
| #4846 | 2 |
| #4833 | 2 |
| #4814 | 2 |
| #4788 | 2 |
| #3107 | 3 |