Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
646 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20252297 | C2 | semidirect |
| 2. #20252035 | C2 | semidirect |
| 3. #20244967 | C2 | semidirect |
| 4. #20244695 | C2 | semidirect |
| 6. #20244098 | C2 | semidirect |
| 7. #20243887 | C2 | semidirect |
| 8. #20243747 | C2 | semidirect |
| 9. #20243672 | C2 | semidirect |
| 10. #20243535 | C2 | semidirect |
| 11. C47×#2098 | C2 | semidirect |
| 189. #2098 | D47 | semidirect |
| 229. C47 | #29387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252297 | 2 |
| #20252035 | 2 |
| #20244967 | 2 |
| #20244695 | 2 |
| #20244492 | 2 |
| #20244098 | 2 |
| #20243887 | 2 |
| #20243747 | 2 |
| #20243672 | 2 |
| #20243535 | 2 |
| C47×#2098 | 2 |
| #29387 | 47 |