Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
194 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 194 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. #20245665 | C2 | semidirect |
| 3. #20241567 | C2 | semidirect |
| 4. #20241566 | C2 | semidirect |
| 5. #20241565 | C2 | semidirect |
| 6. #20241521 | C2 | semidirect |
| 7. C47×#1415 | C2 | semidirect |
| 91. #1415 | D47 | semidirect |
| 109. C47 | #13723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245665 | 2 |
| #20245636 | 2 |
| #20241567 | 2 |
| #20241566 | 2 |
| #20241565 | 2 |
| #20241521 | 2 |
| C47×#1415 | 2 |
| #13723 | 47 |