Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
460 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #20243191 | C2 | semidirect |
| 5. #20243190 | C2 | semidirect |
| 6. #20241517 | C2 | semidirect |
| 7. C47×#1395 | C2 | semidirect |
| 8. C2×#13094032 | C4 | semidirect |
| 15. #15689146 | C4 | semidirect |
| 18. #15689089 | C4 | semidirect |
| 21. C2×C8×Dic47 | C4 | semidirect |
| 22. #15688921 | C4 | semidirect |
| 23. #15688919 | C4 | semidirect |
| 206. #1395 | D47 | semidirect |
| 236. C47 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252096 | 2 |
| #20245071 | 2 |
| #20245051 | 2 |
| #20243191 | 2 |
| #20243190 | 2 |
| #20241517 | 2 |
| C47×#1395 | 2 |
| #12633 | 47 |