Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
906 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20253968 | C2 | semidirect |
| 2. #20253966 | C2 | semidirect |
| 3. #20253817 | C2 | semidirect |
| 4. #20253811 | C2 | semidirect |
| 5. #20243060 | C2 | semidirect |
| 6. #20243058 | C2 | semidirect |
| 7. #20243056 | C2 | semidirect |
| 8. #20243054 | C2 | semidirect |
| 9. #20243052 | C2 | semidirect |
| 10. #322×D47 | C2 | semidirect |
| 11. C47×#1722 | C2 | semidirect |
| 135. C8×D47 | D8 | semidirect |
| 193. #1722 | D47 | semidirect |
| 235. C47 | #19616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253968 | 2 |
| #20253966 | 2 |
| #20253817 | 2 |
| #20253811 | 2 |
| #20243060 | 2 |
| #20243058 | 2 |
| #20243056 | 2 |
| #20243054 | 2 |
| #20243052 | 2 |
| #322×D47 | 2 |
| C47×#1722 | 2 |
| #19616 | 47 |