Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×ΓL(1,𝔽25) | C2 | semidirect |
| 3. #5524 | C2 | semidirect |
| 4. C3×#427 | C2 | semidirect |
| 5. #5002 | C2 | semidirect |
| 6. #4886 | C2 | semidirect |
| 7. #4867 | C2 | semidirect |
| 8. #4865 | C2 | semidirect |
| 15. C2×Dic12 | C22 | semidirect |
| 17. C2×D24 | C22 | semidirect |
| 18. C2×#204 | C22 | semidirect |
| 27. C3×#107 | C22 | semidirect |
| 28. C3×#106 | C22 | semidirect |
| 29. #810 | C22 | semidirect |
| 30. #809 | C22 | semidirect |
| 37. #427 | D3 | semidirect |
| 53. C2×C3×C8 | D4 | semidirect |
| 86. #107 | C2×D3 | semidirect |
| 87. #106 | C2×D3 | semidirect |
| 137. C2×C8 | D12 | semidirect |
| 205. C3 | #3054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| #5524 | 2 |
| C3×#427 | 2 |
| #5002 | 2 |
| #4886 | 2 |
| #4867 | 2 |
| #4865 | 2 |
| #3054 | 3 |