Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
300 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. #20242789 | C2 | semidirect |
| 5. #20241366 | C2 | semidirect |
| 6. #20241352 | C2 | semidirect |
| 7. C47×#2227 | C2 | semidirect |
| 125. #2227 | D47 | semidirect |
| 151. C47 | #12385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256398 | 2 |
| #20245613 | 2 |
| #20242789 | 2 |
| #20241435 | 2 |
| #20241366 | 2 |
| #20241352 | 2 |
| C47×#2227 | 2 |
| #12385 | 47 |