Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #5567 | C2 | semidirect |
| 3. C3×C8×Q8 | C2 | semidirect |
| 4. #4849 | C2 | semidirect |
| 7. #4829 | C2 | semidirect |
| 8. C4×Dic12 | C2 | semidirect |
| 11. #4681 | C2 | semidirect |
| 50. C8×Q8 | D3 | semidirect |
| 226. C3 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5584 | 2 |
| #5567 | 2 |
| C3×C8×Q8 | 2 |
| #4849 | 2 |
| #4846 | 2 |
| #4845 | 2 |
| #4829 | 2 |
| C4×Dic12 | 2 |
| #4697 | 2 |
| C4×#204 | 2 |
| #4681 | 2 |
| #3364 | 3 |