Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20241456 | C2 | semidirect |
| 5. #20241449 | C2 | semidirect |
| 6. #20241427 | C2 | semidirect |
| 7. C47×#2245 | C2 | semidirect |
| 90. #2245 | D47 | semidirect |
| 115. C47 | #12466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245561 | 2 |
| #20245466 | 2 |
| #20245231 | 2 |
| #20241456 | 2 |
| #20241449 | 2 |
| #20241427 | 2 |
| C47×#2245 | 2 |
| #12466 | 47 |