Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
176 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 51 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. #5088 | C2 | semidirect |
| 2. #5084 | C2 | semidirect |
| 4. #4834 | C2 | semidirect |
| 5. C3×#333 | C2 | semidirect |
| 6. #4485 | C2 | semidirect |
| 7. #4480 | C2 | semidirect |
| 29. #333 | D3 | semidirect |
| 159. C3 | #1677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5088 | 2 |
| #5084 | 2 |
| #4843 | 2 |
| #4834 | 2 |
| C3×#333 | 2 |
| #4485 | 2 |
| #4480 | 2 |
| #1677 | 3 |