Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
542 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20242073 | C2 | semidirect |
| 5. #20242060 | C2 | semidirect |
| 6. #20241221 | C2 | semidirect |
| 7. C47×#2862 | C2 | semidirect |
| 171. #2862 | D47 | semidirect |
| 202. C47 | #10286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254516 | 2 |
| #20254509 | 2 |
| #20244216 | 2 |
| #20242073 | 2 |
| #20242060 | 2 |
| #20241221 | 2 |
| C47×#2862 | 2 |
| #10286 | 47 |