Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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. #5721 | C2 | semidirect |
| 3. C3×#462 | C2 | semidirect |
| 4. #5190 | C2 | semidirect |
| 5. #5185 | C2 | semidirect |
| 7. C4×#216 | C2 | semidirect |
| 9. #4831 | C2 | semidirect |
| 10. #4818 | C2 | semidirect |
| 11. #4817 | C2 | semidirect |
| 47. #462 | D3 | semidirect |
| 238. C3 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5721 | 2 |
| #5585 | 2 |
| C3×#462 | 2 |
| #5190 | 2 |
| #5185 | 2 |
| #5085 | 2 |
| C4×#216 | 2 |
| #4848 | 2 |
| #4831 | 2 |
| #4818 | 2 |
| #4817 | 2 |
| #3400 | 3 |