Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 354 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 |
| 3. C3×#476 | C2 | semidirect |
| 4. #5078 | C2 | semidirect |
| 5. C4×#214 | C2 | semidirect |
| 6. #4868 | C2 | semidirect |
| 7. #4861 | C2 | semidirect |
| 8. #4850 | C2 | semidirect |
| 9. #4838 | C2 | semidirect |
| 10. #4780 | C2 | semidirect |
| 11. #4774 | C2 | semidirect |
| 48. #476 | D3 | semidirect |
| 237. C3 | #3357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5730 | 2 |
| #5563 | 2 |
| C3×#476 | 2 |
| #5078 | 2 |
| C4×#214 | 2 |
| #4868 | 2 |
| #4861 | 2 |
| #4850 | 2 |
| #4838 | 2 |
| #4780 | 2 |
| #4774 | 2 |
| #3357 | 3 |