Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
144 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 53 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. #5196 | C2 | semidirect |
| 3. #4895 | C2 | semidirect |
| 4. C3×#359 | C2 | semidirect |
| 5. #4510 | C2 | semidirect |
| 6. #4502 | C2 | semidirect |
| 7. #4493 | C2 | semidirect |
| 16. #829 | C4 | semidirect |
| 17. #828 | C4 | semidirect |
| 18. #827 | C4 | semidirect |
| 19. #826 | C4 | semidirect |
| 29. #359 | D3 | semidirect |
| 138. C3 | #2179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5196 | 2 |
| #5194 | 2 |
| #4895 | 2 |
| C3×#359 | 2 |
| #4510 | 2 |
| #4502 | 2 |
| #4493 | 2 |
| #2179 | 3 |