Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
472 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 181 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×#907 | C2 | semidirect |
| 3. C2×C3×#108 | C2 | semidirect |
| 4. C2×#825 | C2 | semidirect |
| 5. C2×C8×Dic3 | C2 | semidirect |
| 6. #4895 | C2 | direct (N × H) |
| 14. #907 | C22 | semidirect |
| 15. C2×Dic12 | C4 | semidirect |
| 16. #904 | C4 | semidirect |
| 18. C2×D24 | C4 | semidirect |
| 19. C2×#204 | C4 | semidirect |
| 22. C3×#108 | C22 | semidirect |
| 23. #825 | C22 | semidirect |
| 24. C8×Dic3 | C22 | semidirect |
| 28. C2×#108 | D3 | semidirect |
| 54. Dic12 | C2×C4 | semidirect |
| 55. D24 | C2×C4 | semidirect |
| 56. #204 | C2×C4 | semidirect |
| 73. #108 | C2×D3 | semidirect |
| 166. C2×C3 | #443 | semidirect |
| 181. C3 | C2×#443 | semidirect |
| 185. C2 | #4895 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#907 | 2 |
| C2×#904 | 2 |
| C2×C3×#108 | 2 |
| C2×#825 | 2 |
| C2×C8×Dic3 | 2 |
| #4895 | 2 |
| C2×#443 | 3 |