Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
350 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20254837 | C2 | semidirect |
| 5. #20241405 | C2 | semidirect |
| 6. #20241329 | C2 | semidirect |
| 7. C47×#1350 | C2 | semidirect |
| 161. #1350 | D47 | semidirect |
| 187. C47 | #12165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254837 | 2 |
| #20245319 | 2 |
| #20245316 | 2 |
| #20244645 | 2 |
| #20241405 | 2 |
| #20241329 | 2 |
| C47×#1350 | 2 |
| #12165 | 47 |