Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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×#492 | C2 | semidirect |
| 2. #5087 | C2 | semidirect |
| 4. C8×D12 | C2 | semidirect |
| 5. #4547 | C2 | semidirect |
| 6. #4544 | C2 | semidirect |
| 7. #4457 | C2 | semidirect |
| 24. #492 | D3 | semidirect |
| 81. D12 | SD16 | semidirect |
| 85. C3×C8 | D8 | semidirect |
| 145. C8 | #213 | semidirect |
| 165. C3 | #1665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#492 | 2 |
| #5087 | 2 |
| #5072 | 2 |
| C8×D12 | 2 |
| #4547 | 2 |
| #4544 | 2 |
| #4457 | 2 |
| #1665 | 3 |