Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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. C2×C3×C4×Q8 | C2 | semidirect |
| 3. #5231 | C2 | semidirect |
| 4. #4992 | C2 | semidirect |
| 6. #4986 | C2 | semidirect |
| 7. C4×(C2×D3)⋊C4 | C2 | semidirect |
| 8. #4932 | C2 | semidirect |
| 28. C2×C4×Q8 | D3 | semidirect |
| 187. C3 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×Q8 | 2 |
| C2×C4×D12 | 2 |
| #5231 | 2 |
| #4992 | 2 |
| #4991 | 2 |
| #4986 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #4932 | 2 |
| #2398 | 3 |