Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
518 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20253940 | C2 | semidirect |
| 4. #20242014 | C2 | semidirect |
| 5. #20241938 | C2 | semidirect |
| 7. C47×#1288 | C2 | semidirect |
| 196. #1288 | D47 | semidirect |
| 227. C47 | #10023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253940 | 2 |
| #20253488 | 2 |
| #20249259 | 2 |
| #20242014 | 2 |
| #20241938 | 2 |
| #20241832 | 2 |
| C47×#1288 | 2 |
| #10023 | 47 |