Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 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. #20244233 | C2 | semidirect |
| 4. #20241983 | C2 | semidirect |
| 6. #20241279 | C2 | semidirect |
| 7. C47×#3230 | C2 | semidirect |
| 176. #3230 | D47 | semidirect |
| 210. C47 | #10109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254771 | 2 |
| #20253784 | 2 |
| #20244233 | 2 |
| #20241983 | 2 |
| #20241804 | 2 |
| #20241279 | 2 |
| C47×#3230 | 2 |
| #10109 | 47 |