Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 121 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×#541 | C2 | semidirect |
| 3. #5085 | C2 | semidirect |
| 4. #5082 | C2 | semidirect |
| 5. #5067 | C2 | semidirect |
| 6. #5065 | C2 | semidirect |
| 7. #5049 | C2 | semidirect |
| 8. #5048 | C2 | semidirect |
| 9. #5026 | C2 | semidirect |
| 10. C4×#215 | C2 | semidirect |
| 11. #4997 | C2 | semidirect |
| 40. #541 | D3 | semidirect |
| 212. C3 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#541 | 2 |
| #5535 | 2 |
| #5085 | 2 |
| #5082 | 2 |
| #5067 | 2 |
| #5065 | 2 |
| #5049 | 2 |
| #5048 | 2 |
| #5026 | 2 |
| C4×#215 | 2 |
| #4997 | 2 |
| #3174 | 3 |