Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
464 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #20243592 | C2 | semidirect |
| 4. #20243573 | C2 | semidirect |
| 6. #20241236 | C2 | semidirect |
| 7. C47×#1297 | C2 | semidirect |
| 24. #15688859 | C4 | semidirect |
| 25. #15688859 | C4 | semidirect |
| 26. #15688856 | C4 | semidirect |
| 27. #15688856 | C4 | semidirect |
| 215. #1297 | D47 | semidirect |
| 248. C47 | #8875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252438 | 2 |
| #20243688 | 2 |
| #20243592 | 2 |
| #20243573 | 2 |
| #20241877 | 2 |
| #20241236 | 2 |
| C47×#1297 | 2 |
| #8875 | 47 |