Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
814 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 159 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. #20254125 | C2 | semidirect |
| 2. #20254124 | C2 | semidirect |
| 3. #20253846 | C2 | semidirect |
| 4. #20253778 | C2 | semidirect |
| 5. #20243055 | C2 | semidirect |
| 6. #20243049 | C2 | semidirect |
| 7. #20243028 | C2 | semidirect |
| 8. #20243019 | C2 | semidirect |
| 9. #20242989 | C2 | semidirect |
| 10. #20241690 | C2 | semidirect |
| 11. C47×#1709 | C2 | semidirect |
| 189. #1709 | D47 | semidirect |
| 228. C47 | #19750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254125 | 2 |
| #20254124 | 2 |
| #20253846 | 2 |
| #20253778 | 2 |
| #20243055 | 2 |
| #20243049 | 2 |
| #20243028 | 2 |
| #20243019 | 2 |
| #20242989 | 2 |
| #20241690 | 2 |
| C47×#1709 | 2 |
| #19750 | 47 |