Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20243525 | C2 | semidirect |
| 5. #20241279 | C2 | semidirect |
| 6. #20241224 | C2 | semidirect |
| 7. C47×#1574 | C2 | semidirect |
| 164. #1574 | D47 | semidirect |
| 195. C47 | #8900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252509 | 2 |
| #20243525 | 2 |
| #20241825 | 2 |
| #20241768 | 2 |
| #20241279 | 2 |
| #20241224 | 2 |
| C47×#1574 | 2 |
| #8900 | 47 |