Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
654 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20252298 | C2 | semidirect |
| 2. #20252028 | C2 | semidirect |
| 3. #20244969 | C2 | semidirect |
| 4. #20244941 | C2 | semidirect |
| 5. #20244691 | C2 | semidirect |
| 6. #20244095 | C2 | semidirect |
| 7. #20243891 | C2 | semidirect |
| 8. #20243752 | C2 | semidirect |
| 9. #20243673 | C2 | semidirect |
| 10. #20243538 | C2 | semidirect |
| 229. C47 | #29386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252298 | 2 |
| #20252028 | 2 |
| #20244969 | 2 |
| #20244941 | 2 |
| #20244691 | 2 |
| #20244095 | 2 |
| #20243891 | 2 |
| #20243752 | 2 |
| #20243673 | 2 |
| #20243538 | 2 |
| C47×#2017 | 2 |
| #29386 | 47 |