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. #20253966 | C2 | semidirect |
| 2. #20253965 | C2 | semidirect |
| 3. #20253815 | C2 | semidirect |
| 4. #20253811 | C2 | semidirect |
| 5. #20243061 | C2 | semidirect |
| 6. #20243059 | C2 | semidirect |
| 7. #20243057 | C2 | semidirect |
| 8. #20243055 | C2 | semidirect |
| 9. #20243053 | C2 | semidirect |
| 10. #322×D47 | C2 | semidirect |
| 11. C47×#1721 | C2 | semidirect |
| 135. C8×D47 | D8 | semidirect |
| 196. #1721 | 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 |
|---|---|
| #20253966 | 2 |
| #20253965 | 2 |
| #20253815 | 2 |
| #20253811 | 2 |
| #20243061 | 2 |
| #20243059 | 2 |
| #20243057 | 2 |
| #20243055 | 2 |
| #20243053 | 2 |
| #322×D47 | 2 |
| C47×#1721 | 2 |
| #19616 | 47 |