Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×D24 | C2 | semidirect |
| 2. C22×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C2×#895 | C2 | semidirect |
| 4. C2×C3×#106 | C2 | semidirect |
| 5. C2×#809 | C2 | semidirect |
| 6. #4865 | C2 | direct (N × H) |
| 16. C2×D24 | C22 | semidirect |
| 18. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 20. #895 | C22 | semidirect |
| 21. C3×#106 | C22 | semidirect |
| 22. #809 | C22 | semidirect |
| 27. C2×#106 | D3 | semidirect |
| 44. C2×C3×C8 | D4 | semidirect |
| 66. #106 | C2×D3 | semidirect |
| 91. C3×C8 | C2×D4 | semidirect |
| 112. C2×C8 | D12 | semidirect |
| 156. C8 | C2×D12 | semidirect |
| 157. C2×C3 | #469 | semidirect |
| 177. C3 | C2×#469 | semidirect |
| 180. C2 | #4865 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D24 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| C2×#895 | 2 |
| C2×C3×#106 | 2 |
| C2×#809 | 2 |
| #4865 | 2 |
| C2×#469 | 3 |