Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
| 2. #5713 | C2 | semidirect |
| 3. C3×#486 | C2 | semidirect |
| 4. #5091 | C2 | semidirect |
| 6. #4787 | C2 | semidirect |
| 7. #4768 | C2 | semidirect |
| 8. #4763 | C2 | semidirect |
| 9. #4756 | C2 | semidirect |
| 10. C4×#204 | C2 | semidirect |
| 11. C8×Dic6 | C2 | semidirect |
| 45. #486 | D3 | semidirect |
| 239. C3 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5730 | 2 |
| #5713 | 2 |
| C3×#486 | 2 |
| #5091 | 2 |
| #5072 | 2 |
| #4787 | 2 |
| #4768 | 2 |
| #4763 | 2 |
| #4756 | 2 |
| C4×#204 | 2 |
| C8×Dic6 | 2 |
| #3361 | 3 |