Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
176 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 53 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×#486 | C2 | semidirect |
| 2. #5084 | C2 | semidirect |
| 4. C8×D12 | C2 | semidirect |
| 5. #4546 | C2 | semidirect |
| 6. #4544 | C2 | semidirect |
| 7. #4457 | C2 | semidirect |
| 24. #486 | D3 | semidirect |
| 159. C3 | #1677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#486 | 2 |
| #5084 | 2 |
| #5072 | 2 |
| C8×D12 | 2 |
| #4546 | 2 |
| #4544 | 2 |
| #4457 | 2 |
| #1677 | 3 |