Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #4851 | C2 | semidirect |
| 5. #4850 | C2 | semidirect |
| 7. #4703 | C2 | semidirect |
| 8. #4702 | C2 | semidirect |
| 192. C3 | #3237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5470 | 2 |
| C3×#432 | 2 |
| #4851 | 2 |
| #4850 | 2 |
| #4723 | 2 |
| #4703 | 2 |
| #4702 | 2 |
| #3237 | 3 |