Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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. #4925 | C2 | semidirect |
| 4. #4451 | C2 | semidirect |
| 13. #874 | C4 | semidirect |
| 15. C4×D12 | C4 | semidirect |
| 16. #869 | C4 | semidirect |
| 23. C4×C4⋊C4 | D3 | semidirect |
| 172. C3 | #1502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5477 | 2 |
| C3×C4×C4⋊C4 | 2 |
| #4925 | 2 |
| #4451 | 2 |
| #1502 | 3 |