Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
398 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20251217 | C2 | semidirect |
| 2. #20242425 | C2 | semidirect |
| 4. #20241414 | C2 | semidirect |
| 5. #20241390 | C2 | semidirect |
| 6. #20241334 | C2 | semidirect |
| 7. C47×#2039 | C2 | semidirect |
| 185. #2039 | D47 | semidirect |
| 217. C47 | #12144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251217 | 2 |
| #20242425 | 2 |
| #20242323 | 2 |
| #20241414 | 2 |
| #20241390 | 2 |
| #20241334 | 2 |
| C47×#2039 | 2 |
| #12144 | 47 |