Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
560 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
| 3. #4990 | C2 | semidirect |
| 5. #4936 | C2 | semidirect |
| 6. C4×C4⋊Dic3 | C2 | semidirect |
| 7. #4666 | C2 | semidirect |
| 8. #4664 | C2 | semidirect |
| 21. C4×D12 | C4 | semidirect |
| 33. C4×C4⋊C4 | D3 | semidirect |
| 188. C3 | #2357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D12 | 2 |
| C3×C4×C4⋊C4 | 2 |
| #4990 | 2 |
| #4939 | 2 |
| #4936 | 2 |
| C4×C4⋊Dic3 | 2 |
| #4666 | 2 |
| #4664 | 2 |
| #2357 | 3 |