Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #20244176 | C2 | semidirect |
| 5. #20241481 | C2 | semidirect |
| 6. #20241478 | C2 | semidirect |
| 7. C47×#2161 | C2 | semidirect |
| 17. #15688940 | C4 | semidirect |
| 18. #15688937 | C4 | semidirect |
| 138. #2161 | D47 | semidirect |
| 166. C47 | #12942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252304 | 2 |
| #20245138 | 2 |
| C2×#15688929 | 2 |
| #20244176 | 2 |
| #20241481 | 2 |
| #20241478 | 2 |
| C47×#2161 | 2 |
| #12942 | 47 |