Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #5745 | C2 | semidirect |
| 3. #5129 | C2 | semidirect |
| 4. #5005 | C2 | semidirect |
| 5. #5002 | C2 | semidirect |
| 6. C3×#344 | C2 | semidirect |
| 7. #4558 | C2 | semidirect |
| 17. #909 | C4 | semidirect |
| 19. #908 | C4 | semidirect |
| 33. #344 | D3 | semidirect |
| 230. C3 | #1881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5748 | 2 |
| #5745 | 2 |
| #5129 | 2 |
| #5005 | 2 |
| #5002 | 2 |
| C3×#344 | 2 |
| #4558 | 2 |
| #1881 | 3 |