Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
436 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 436 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 |
|---|---|---|
| 4. #20241816 | C2 | semidirect |
| 5. #20241731 | C2 | semidirect |
| 6. #20241251 | C2 | semidirect |
| 7. C47×#1307 | C2 | semidirect |
| 168. #1307 | D47 | semidirect |
| 196. C47 | #9527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253511 | 2 |
| #20252466 | 2 |
| #20242108 | 2 |
| #20241816 | 2 |
| #20241731 | 2 |
| #20241251 | 2 |
| C47×#1307 | 2 |
| #9527 | 47 |