Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20242546 | C2 | semidirect |
| 4. #20242484 | C2 | semidirect |
| 5. #20242126 | C2 | semidirect |
| 6. #20241843 | C2 | semidirect |
| 7. C47×#3556 | C2 | semidirect |
| 152. #3556 | D47 | semidirect |
| 185. C47 | #18698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254771 | 2 |
| #20253713 | 2 |
| #20242546 | 2 |
| #20242484 | 2 |
| #20242126 | 2 |
| #20241843 | 2 |
| C47×#3556 | 2 |
| #18698 | 47 |