Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
324 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#15688952 | C2 | semidirect |
| 5. #20243269 | C2 | semidirect |
| 6. #20241465 | C2 | semidirect |
| 7. C47×#1382 | C2 | semidirect |
| 17. #15688926 | C4 | semidirect |
| 18. #15688926 | C4 | semidirect |
| 19. #15688923 | C4 | semidirect |
| 20. #15688923 | C4 | semidirect |
| 153. #1382 | D47 | semidirect |
| 178. C47 | #13134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688952 | 2 |
| C2×#15688931 | 2 |
| #20245093 | 2 |
| #20244274 | 2 |
| #20243269 | 2 |
| #20241465 | 2 |
| C47×#1382 | 2 |
| #13134 | 47 |