Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. #4849 | C2 | semidirect |
| 4. C8×Dic6 | C2 | semidirect |
| 5. C3×#335 | C2 | semidirect |
| 7. #4482 | C2 | semidirect |
| 28. #335 | D3 | semidirect |
| 152. C3 | #1682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4849 | 2 |
| #4848 | 2 |
| #4694 | 2 |
| C8×Dic6 | 2 |
| C3×#335 | 2 |
| #4485 | 2 |
| #4482 | 2 |
| #1682 | 3 |