Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 3. #20243432 | C2 | semidirect |
| 4. #20241509 | C2 | semidirect |
| 5. C47×#1391 | C2 | semidirect |
| 6. C2×#13094032 | C4 | semidirect |
| 12. #15689146 | C4 | semidirect |
| 14. #15689089 | C4 | semidirect |
| 15. C2×C8×Dic47 | C4 | semidirect |
| 150. #1391 | D47 | semidirect |
| 171. C47 | #12807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252096 | 2 |
| #20245051 | 2 |
| #20243432 | 2 |
| #20241509 | 2 |
| C47×#1391 | 2 |
| #12807 | 47 |