Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
576 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20242012 | C2 | semidirect |
| 3. #20241895 | C2 | semidirect |
| 4. #20241281 | C2 | semidirect |
| 5. C47×#2372 | C2 | semidirect |
| 9. #15689518 | C4 | semidirect |
| 10. #15689513 | C4 | semidirect |
| 33. #13094024 | C2×C4 | semidirect |
| 34. #13094021 | C2×C4 | semidirect |
| 41. #13093935 | C2×C4 | semidirect |
| 166. #2372 | D47 | semidirect |
| 193. C47 | #9441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253852 | 2 |
| #20242012 | 2 |
| #20241895 | 2 |
| #20241281 | 2 |
| C47×#2372 | 2 |
| #9441 | 47 |