Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
366 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 117 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. #5514 | C2 | semidirect |
| 2. C2×C3×#107 | C2 | semidirect |
| 3. #5115 | C2 | semidirect |
| 4. C8×#67 | C2 | semidirect |
| 5. #4968 | C2 | semidirect |
| 6. #4891 | C2 | semidirect |
| 7. #4885 | C2 | semidirect |
| 8. #4883 | C2 | semidirect |
| 9. #4880 | C2 | semidirect |
| 10. #4878 | C2 | semidirect |
| 11. #4872 | C2 | semidirect |
| 50. C2×#107 | D3 | semidirect |
| 234. C3 | #3339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5514 | 2 |
| C2×C3×#107 | 2 |
| #5115 | 2 |
| C8×#67 | 2 |
| #4968 | 2 |
| #4891 | 2 |
| #4885 | 2 |
| #4883 | 2 |
| #4880 | 2 |
| #4878 | 2 |
| #4872 | 2 |
| #3339 | 3 |