Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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. C3×C4×C4⋊C4 | C2 | semidirect |
| 4. #4924 | C2 | semidirect |
| 5. #4523 | C2 | semidirect |
| 15. C4×D12 | C4 | semidirect |
| 16. C4×D12 | C4 | semidirect |
| 19. C4×Dic6 | C4 | semidirect |
| 20. C4×Dic6 | C4 | semidirect |
| 28. C4×C4⋊C4 | D3 | semidirect |
| 105. D12 | C4⋊C4 | semidirect |
| 111. Dic6 | C4⋊C4 | semidirect |
| 159. C3×C4 | #104 | semidirect |
| 219. C4 | #805 | semidirect |
| 224. C3 | #1806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#235 | 2 |
| C3×C4×C4⋊C4 | 2 |
| C2×#805 | 2 |
| #4924 | 2 |
| #4523 | 2 |
| #1806 | 3 |