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 |
|---|---|---|
| 3. #5082 | C2 | semidirect |
| 4. #5081 | C2 | semidirect |
| 6. #5021 | C2 | semidirect |
| 7. #5020 | 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 |
|---|---|
| C3×#533 | 2 |
| #5470 | 2 |
| #5082 | 2 |
| #5081 | 2 |
| #5045 | 2 |
| #5021 | 2 |
| #5020 | 2 |
| #4926 | 2 |
| #3237 | 3 |