Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 57 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. C3×#487 | C2 | semidirect |
| 2. #5093 | C2 | semidirect |
| 5. #5079 | C2 | semidirect |
| 7. C8×C3⋊C8 | C2 | semidirect |
| 24. #487 | D3 | semidirect |
| 130. C3 | #1711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#487 | 2 |
| #5093 | 2 |
| #5088 | 2 |
| #5079 | 2 |
| #4694 | 2 |
| C8×C3⋊C8 | 2 |
| #1711 | 3 |