Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
354 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #20243562 | C2 | semidirect |
| 3. #20242155 | C2 | semidirect |
| 6. #20241288 | C2 | semidirect |
| 7. C47×#1299 | C2 | semidirect |
| 170. #1299 | D47 | semidirect |
| 199. C47 | #8916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252555 | 2 |
| #20243562 | 2 |
| #20242155 | 2 |
| #20241977 | 2 |
| #20241854 | 2 |
| #20241288 | 2 |
| C47×#1299 | 2 |
| #8916 | 47 |