Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
360 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 1. #20245177 | C2 | semidirect |
| 5. #20241498 | C2 | semidirect |
| 6. #20241470 | C2 | semidirect |
| 7. C47×#1772 | C2 | semidirect |
| 16. #15688935 | C4 | semidirect |
| 148. #1772 | D47 | semidirect |
| 173. C47 | #13136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245177 | 2 |
| C2×#15688935 | 2 |
| #20245103 | 2 |
| #20244254 | 2 |
| #20241498 | 2 |
| #20241470 | 2 |
| C47×#1772 | 2 |
| #13136 | 47 |