Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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. C3×#519 | C2 | semidirect |
| 3. #5227 | C2 | semidirect |
| 4. #5027 | C2 | semidirect |
| 5. #5026 | C2 | semidirect |
| 6. C4×#215 | C2 | semidirect |
| 7. #5022 | C2 | semidirect |
| 8. #5003 | C2 | semidirect |
| 9. #5000 | C2 | semidirect |
| 37. #519 | D3 | semidirect |
| 198. C3 | #3126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#519 | 2 |
| #5535 | 2 |
| #5227 | 2 |
| #5027 | 2 |
| #5026 | 2 |
| C4×#215 | 2 |
| #5022 | 2 |
| #5003 | 2 |
| #5000 | 2 |
| #3126 | 3 |