Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 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×#13093934 | C4 | semidirect |
| 145. #1391 | D47 | semidirect |
| 166. C47 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252103 | 2 |
| #20245051 | 2 |
| #20243432 | 2 |
| #20241509 | 2 |
| C47×#1391 | 2 |
| #12808 | 47 |