Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
172 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20245664 | C2 | semidirect |
| 5. #20241463 | C2 | semidirect |
| 6. #20241450 | C2 | semidirect |
| 7. C47×#1366 | C2 | semidirect |
| 89. #1366 | D47 | semidirect |
| 108. C47 | #12464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245664 | 2 |
| #20245565 | 2 |
| #20245561 | 2 |
| #20245224 | 2 |
| #20241463 | 2 |
| #20241450 | 2 |
| C47×#1366 | 2 |
| #12464 | 47 |