Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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. #5031 | C2 | semidirect |
| 4. #4682 | C2 | semidirect |
| 5. C3×Q8⋊C8 | C2 | semidirect |
| 6. #4486 | C2 | semidirect |
| 31. Q8⋊C8 | D3 | semidirect |
| 87. D12 | Q16 | semidirect |
| 180. C3 | #1649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D12 | 2 |
| #5031 | 2 |
| #4846 | 2 |
| #4682 | 2 |
| C3×Q8⋊C8 | 2 |
| #4486 | 2 |
| #4459 | 2 |
| #1649 | 3 |