Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×D24 | C2 | semidirect |
| 3. C2×C3×M32 | C2 | semidirect |
| 4. #4908 | C2 | direct (N × H) |
| 5. C2×#800 | C2 | semidirect |
| 6. C2×D48 | C2 | semidirect |
| 11. C2×Dic12 | C22 | semidirect |
| 13. #904 | C22 | semidirect |
| 17. C2×D24 | C22 | semidirect |
| 18. C2×D24 | C22 | semidirect |
| 20. C3×M32 | C22 | semidirect |
| 21. C2×C3×C16 | C22 | semidirect |
| 22. #800 | C22 | semidirect |
| 23. D48 | C22 | semidirect |
| 29. C2×M32 | D3 | semidirect |
| 47. Dic12 | C23 | semidirect |
| 52. D24 | C23 | semidirect |
| 54. C3×C16 | C23 | semidirect |
| 69. M32 | C2×D3 | semidirect |
| 70. C2×C16 | C2×D3 | semidirect |
| 117. C16 | C22×D3 | semidirect |
| 153. C2×C3 | #509 | semidirect |
| 169. C3 | C2×#509 | semidirect |
| 173. C2 | #4908 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| C22×D24 | 2 |
| C2×C3×M32 | 2 |
| #4908 | 2 |
| C2×#800 | 2 |
| C2×D48 | 2 |
| C2×#509 | 3 |