Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
798 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 798 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. #20253946 | C2 | semidirect |
| 2. #20253945 | C2 | semidirect |
| 3. #20253897 | C2 | semidirect |
| 5. #20243022 | C2 | semidirect |
| 6. #20243021 | C2 | semidirect |
| 7. #20243014 | C2 | semidirect |
| 8. #20243009 | C2 | semidirect |
| 9. #20243008 | C2 | semidirect |
| 10. #322×D47 | C2 | semidirect |
| 11. C47×#1715 | C2 | semidirect |
| 130. C8×D47 | SD16 | semidirect |
| 183. #1715 | D47 | semidirect |
| 223. C47 | #19608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253946 | 2 |
| #20253945 | 2 |
| #20253897 | 2 |
| #20253815 | 2 |
| #20243022 | 2 |
| #20243021 | 2 |
| #20243014 | 2 |
| #20243009 | 2 |
| #20243008 | 2 |
| #322×D47 | 2 |
| C47×#1715 | 2 |
| #19608 | 47 |