Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
640 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 640 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. #20251871 | C2 | semidirect |
| 3. #20245079 | C2 | semidirect |
| 4. #20245037 | C2 | semidirect |
| 5. #20241516 | C2 | semidirect |
| 6. #20241510 | C2 | semidirect |
| 7. C47×#1796 | C2 | semidirect |
| 8. C2×#13094049 | C4 | semidirect |
| 9. C22×#10625336 | C4 | semidirect |
| 16. #15689132 | C4 | semidirect |
| 17. #15689119 | C4 | semidirect |
| 243. #1796 | D47 | semidirect |
| 276. C47 | #13098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252674 | 2 |
| #20251871 | 2 |
| #20245079 | 2 |
| #20245037 | 2 |
| #20241516 | 2 |
| #20241510 | 2 |
| C47×#1796 | 2 |
| #13098 | 47 |