Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 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. #20242105 | C2 | semidirect |
| 5. #20241299 | C2 | semidirect |
| 6. #20241260 | C2 | semidirect |
| 7. C47×#1997 | C2 | semidirect |
| 176. #1997 | D47 | semidirect |
| 211. C47 | #9338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254609 | 2 |
| #20252555 | 2 |
| #20242105 | 2 |
| #20241993 | 2 |
| #20241299 | 2 |
| #20241260 | 2 |
| C47×#1997 | 2 |
| #9338 | 47 |