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. #20253950 | C2 | semidirect |
| 2. #20253949 | C2 | semidirect |
| 3. #20253897 | C2 | semidirect |
| 5. #20243019 | C2 | semidirect |
| 6. #20243017 | C2 | semidirect |
| 7. #20243016 | C2 | semidirect |
| 8. #20243013 | C2 | semidirect |
| 9. #20243012 | C2 | semidirect |
| 10. #322×D47 | C2 | semidirect |
| 11. C47×#1716 | C2 | semidirect |
| 130. C8×D47 | SD16 | semidirect |
| 181. #1716 | 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 |
|---|---|
| #20253950 | 2 |
| #20253949 | 2 |
| #20253897 | 2 |
| #20253817 | 2 |
| #20243019 | 2 |
| #20243017 | 2 |
| #20243016 | 2 |
| #20243013 | 2 |
| #20243012 | 2 |
| #322×D47 | 2 |
| C47×#1716 | 2 |
| #19608 | 47 |