Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #20245162 | C2 | semidirect |
| 5. #20241504 | C2 | semidirect |
| 6. #20241503 | C2 | semidirect |
| 7. C47×#2155 | C2 | semidirect |
| 18. #15688904 | C4 | semidirect |
| 41. #13093964 | C2×C4 | semidirect |
| 54. M32×C47 | C2×C4 | semidirect |
| 146. #2155 | D47 | semidirect |
| 172. C47 | #12932 | semidirect |
| 195. M32 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251976 | 2 |
| #20245162 | 2 |
| C2×#15688904 | 2 |
| #20243427 | 2 |
| #20241504 | 2 |
| #20241503 | 2 |
| C47×#2155 | 2 |
| #12932 | 47 |