Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
300 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20245154 | C2 | semidirect |
| 4. C2×#15688900 | C2 | semidirect |
| 6. #20241471 | C2 | semidirect |
| 7. C47×#1378 | C2 | semidirect |
| 139. #1378 | D47 | semidirect |
| 161. C47 | #13127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245154 | 2 |
| #20245017 | 2 |
| #20245008 | 2 |
| C2×#15688900 | 2 |
| #20243234 | 2 |
| #20241471 | 2 |
| C47×#1378 | 2 |
| #13127 | 47 |