Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 3. #5122 | C2 | semidirect |
| 5. #4964 | C2 | semidirect |
| 6. C3×#343 | C2 | semidirect |
| 7. #4558 | C2 | semidirect |
| 16. #823 | C4 | semidirect |
| 30. #343 | D3 | semidirect |
| 194. C3 | #1931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5131 | 2 |
| C2×#823 | 2 |
| #5122 | 2 |
| C2×#809 | 2 |
| #4964 | 2 |
| C3×#343 | 2 |
| #4558 | 2 |
| #1931 | 3 |