Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#204 | C2 | semidirect |
| 2. C2×#901 | C2 | semidirect |
| 3. #5526 | C2 | semidirect |
| 5. C3×#427 | C2 | semidirect |
| 6. #5004 | C2 | semidirect |
| 7. #5001 | C2 | semidirect |
| 8. #4886 | C2 | semidirect |
| 9. #4864 | C2 | semidirect |
| 22. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 23. C2×D3×C8 | C22 | semidirect |
| 24. #897 | C22 | semidirect |
| 32. C3×#107 | C22 | semidirect |
| 33. C3×#106 | C22 | semidirect |
| 34. #810 | C22 | semidirect |
| 42. #427 | D3 | semidirect |
| 63. C2×C3×C8 | D4 | semidirect |
| 102. #107 | C2×D3 | semidirect |
| 103. #106 | C2×D3 | semidirect |
| 159. C2×C8 | D12 | semidirect |
| 235. C3 | #3057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#204 | 2 |
| C2×#901 | 2 |
| #5526 | 2 |
| #5525 | 2 |
| C3×#427 | 2 |
| #5004 | 2 |
| #5001 | 2 |
| #4886 | 2 |
| #4864 | 2 |
| #3057 | 3 |