Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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×#15688946 | C2 | semidirect |
| 5. #20243285 | C2 | semidirect |
| 6. #20241497 | C2 | semidirect |
| 7. C47×#1375 | C2 | semidirect |
| 17. #15688928 | C4 | semidirect |
| 18. #15688925 | C4 | semidirect |
| 149. #1375 | D47 | semidirect |
| 171. C47 | #13143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688946 | 2 |
| C2×#15688934 | 2 |
| #20245101 | 2 |
| #20244281 | 2 |
| #20243285 | 2 |
| #20241497 | 2 |
| C47×#1375 | 2 |
| #13143 | 47 |