Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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×#446 | C2 | semidirect |
| 4. #4851 | C2 | semidirect |
| 5. #4850 | C2 | semidirect |
| 9. #4702 | C2 | semidirect |
| 11. #4682 | C2 | semidirect |
| 50. #446 | D3 | semidirect |
| 84. #204 | Q8 | semidirect |
| 134. Dic6 | C2×Q8 | semidirect |
| 137. C3×C8 | C2×Q8 | semidirect |
| 208. C8 | D3×Q8 | semidirect |
| 228. C3 | #3386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D12 | 2 |
| #5567 | 2 |
| C3×#446 | 2 |
| #4851 | 2 |
| #4850 | 2 |
| #4847 | 2 |
| #4846 | 2 |
| #4710 | 2 |
| #4702 | 2 |
| C4×#204 | 2 |
| #4682 | 2 |
| #3386 | 3 |