Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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×Q16 | C2 | semidirect |
| 4. #5183 | C2 | semidirect |
| 5. #5030 | C2 | semidirect |
| 7. #4878 | C2 | semidirect |
| 9. #4797 | C2 | semidirect |
| 10. C4×Dic12 | C2 | semidirect |
| 49. C4×Q16 | D3 | semidirect |
| 218. C3 | #3177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5583 | 2 |
| C3×C4×Q16 | 2 |
| #5188 | 2 |
| #5183 | 2 |
| #5030 | 2 |
| #4887 | 2 |
| #4878 | 2 |
| #4816 | 2 |
| #4797 | 2 |
| C4×Dic12 | 2 |
| #4689 | 2 |
| #3177 | 3 |