Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
652 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 217 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 |
|---|---|---|
| 2. C2×#872 | C2 | semidirect |
| 3. C3×C4×C4⋊C4 | C2 | semidirect |
| 5. #4972 | C2 | semidirect |
| 6. C4×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C42×Dic3 | C2 | semidirect |
| 8. #4669 | C2 | semidirect |
| 24. C4×D12 | C4 | semidirect |
| 33. C4×C4⋊C4 | D3 | semidirect |
| 60. C4×Dic3 | D4 | semidirect |
| 143. C3×C4 | #117 | semidirect |
| 196. C4 | #872 | semidirect |
| 198. C3 | #2293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D12 | 2 |
| C2×#872 | 2 |
| C3×C4×C4⋊C4 | 2 |
| #4988 | 2 |
| #4972 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| C42×Dic3 | 2 |
| #4669 | 2 |
| #2293 | 3 |