Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
304 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20243143 | C2 | semidirect |
| 3. #20241383 | C2 | semidirect |
| 5. #20241377 | C2 | semidirect |
| 7. C47×#2166 | C2 | semidirect |
| 9. #15689521 | C4 | semidirect |
| 10. #15689507 | C4 | semidirect |
| 15. #15689236 | C4 | semidirect |
| 16. #15689231 | C4 | semidirect |
| 142. #2166 | D47 | semidirect |
| 171. C47 | #11769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254005 | 2 |
| #20243143 | 2 |
| #20241383 | 2 |
| #20241380 | 2 |
| #20241377 | 2 |
| #20241374 | 2 |
| C47×#2166 | 2 |
| #11769 | 47 |