Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1512 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 549 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. C2×#1009 | C2 | semidirect |
| 2. C2×C3×#131 | C2 | semidirect |
| 3. #5752 | C2 | direct (N × H) |
| 4. C2×#908 | C2 | semidirect |
| 5. C2×#904 | C2 | semidirect |
| 6. C22×D24 | C2 | semidirect |
| 10. #1009 | C22 | semidirect |
| 13. C2×#235 | C22 | semidirect |
| 14. C22×D12 | C22 | semidirect |
| 15. C3×#131 | C22 | semidirect |
| 16. C2×C3×M16 | C22 | semidirect |
| 17. C22×C3×C8 | C22 | semidirect |
| 18. #908 | C22 | semidirect |
| 19. C2×Dic12 | C22 | semidirect |
| 20. #904 | C22 | semidirect |
| 21. C2×D24 | C22 | semidirect |
| 22. C2×D24 | C22 | semidirect |
| 23. C2×D24 | C22 | semidirect |
| 24. C2×#204 | C22 | semidirect |
| 30. C2×#131 | D3 | semidirect |
| 41. #235 | C23 | semidirect |
| 45. C2×D12 | C23 | semidirect |
| 48. C3×M16 | C23 | semidirect |
| 51. C2×C3×C8 | C23 | semidirect |
| 52. Dic12 | C23 | semidirect |
| 53. D24 | C23 | semidirect |
| 54. D24 | C23 | semidirect |
| 55. #204 | C23 | semidirect |
| 70. #131 | C2×D3 | semidirect |
| 71. C2×M16 | C2×D3 | semidirect |
| 72. C22×C8 | C2×D3 | semidirect |
| 114. M16 | C22×D3 | semidirect |
| 117. C2×C8 | C22×D3 | semidirect |
| 149. C2×C3 | #576 | semidirect |
| 162. C3 | C2×#576 | semidirect |
| 165. C2 | #5752 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1009 | 2 |
| C2×C3×#131 | 2 |
| #5752 | 2 |
| C2×#908 | 2 |
| C2×#904 | 2 |
| C22×D24 | 2 |
| C2×#576 | 3 |