Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
360 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 360 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. #20244346 | C2 | semidirect |
| 2. #20242174 | C2 | semidirect |
| 5. #20241744 | C2 | semidirect |
| 6. #20241245 | C2 | semidirect |
| 198. C47 | #10509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244346 | 2 |
| #20242174 | 2 |
| #20242083 | 2 |
| #20241883 | 2 |
| #20241744 | 2 |
| #20241245 | 2 |
| C47×#3234 | 2 |
| #10509 | 47 |