Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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×#476 | C2 | semidirect |
| 4. #5091 | C2 | semidirect |
| 5. #5019 | C2 | semidirect |
| 6. #4868 | C2 | semidirect |
| 7. #4853 | C2 | semidirect |
| 8. #4849 | C2 | semidirect |
| 9. #4835 | C2 | semidirect |
| 11. #4757 | C2 | semidirect |
| 48. #476 | D3 | semidirect |
| 267. C3 | #3116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| C4×#237 | 2 |
| C3×#476 | 2 |
| #5091 | 2 |
| #5019 | 2 |
| #4868 | 2 |
| #4853 | 2 |
| #4849 | 2 |
| #4835 | 2 |
| #4783 | 2 |
| #4757 | 2 |
| #3116 | 3 |