Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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×#556 | C2 | semidirect |
| 2. Q8×D12 | C2 | semidirect |
| 3. #5083 | C2 | semidirect |
| 4. #5079 | C2 | semidirect |
| 6. #5055 | C2 | semidirect |
| 7. #5026 | C2 | semidirect |
| 8. #5024 | C2 | semidirect |
| 9. #5021 | C2 | semidirect |
| 11. #5007 | C2 | semidirect |
| 42. #556 | D3 | semidirect |
| 239. C3 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#556 | 2 |
| Q8×D12 | 2 |
| #5083 | 2 |
| #5079 | 2 |
| #5057 | 2 |
| #5055 | 2 |
| #5026 | 2 |
| #5024 | 2 |
| #5021 | 2 |
| C4×#213 | 2 |
| #5007 | 2 |
| #3367 | 3 |