Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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×#904 | C2 | semidirect |
| 2. C2×C3×M32 | C2 | semidirect |
| 3. #4909 | C2 | semidirect |
| 4. #4908 | C2 | semidirect |
| 5. #4904 | C2 | semidirect |
| 9. C2×Dic12 | C22 | semidirect |
| 13. #904 | C22 | semidirect |
| 14. C2×D24 | C22 | semidirect |
| 16. C3×M32 | C22 | semidirect |
| 17. C2×C3×C16 | C22 | semidirect |
| 18. Dic24 | C22 | semidirect |
| 19. #800 | C22 | semidirect |
| 20. D48 | C22 | semidirect |
| 25. C2×M32 | D3 | semidirect |
| 58. M32 | C2×D3 | semidirect |
| 59. C2×C16 | C2×D3 | semidirect |
| 138. C3 | #3414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| C2×C3×M32 | 2 |
| #4909 | 2 |
| #4908 | 2 |
| #4904 | 2 |
| #3414 | 3 |