Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20241939 | C2 | semidirect |
| 5. #20241259 | C2 | semidirect |
| 6. #20241254 | C2 | semidirect |
| 7. C47×#1537 | C2 | semidirect |
| 9. #15689526 | C4 | semidirect |
| 10. #15689497 | C4 | semidirect |
| 11. #15689473 | C4 | semidirect |
| 12. #15689471 | C4 | semidirect |
| 157. #1537 | D47 | semidirect |
| 186. C47 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254107 | 2 |
| #20252458 | 2 |
| #20241939 | 2 |
| #20241936 | 2 |
| #20241259 | 2 |
| #20241254 | 2 |
| C47×#1537 | 2 |
| #9415 | 47 |