Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
268 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20245615 | C2 | semidirect |
| 4. #20243005 | C2 | semidirect |
| 6. #20241304 | C2 | semidirect |
| 7. C47×#2241 | C2 | semidirect |
| 100. #2241 | D47 | semidirect |
| 125. C47 | #12512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245615 | 2 |
| #20245613 | 2 |
| #20245612 | 2 |
| #20243005 | 2 |
| #20242995 | 2 |
| #20241304 | 2 |
| C47×#2241 | 2 |
| #12512 | 47 |