Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #5732 | C2 | semidirect |
| 3. C3×#500 | C2 | semidirect |
| 4. #5094 | C2 | semidirect |
| 5. #5087 | C2 | semidirect |
| 6. #4886 | C2 | semidirect |
| 7. #4885 | C2 | semidirect |
| 8. #4884 | C2 | semidirect |
| 9. #4881 | C2 | semidirect |
| 10. C4×#204 | C2 | semidirect |
| 11. #4688 | C2 | semidirect |
| 44. #500 | D3 | semidirect |
| 139. C3×C8 | #41 | semidirect |
| 216. C8 | #239 | semidirect |
| 239. C3 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5732 | 2 |
| #5726 | 2 |
| C3×#500 | 2 |
| #5094 | 2 |
| #5087 | 2 |
| #4886 | 2 |
| #4885 | 2 |
| #4884 | 2 |
| #4881 | 2 |
| C4×#204 | 2 |
| #4688 | 2 |
| #3353 | 3 |