Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
946 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 946 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 1. #20257788 | C2 | semidirect |
| 2. #20254766 | C2 | semidirect |
| 3. #20242536 | C2 | semidirect |
| 4. #20242474 | C2 | semidirect |
| 5. #20242126 | C2 | semidirect |
| 6. #20241840 | C2 | semidirect |
| 7. C47×#3131 | C2 | semidirect |
| 167. #3131 | D47 | semidirect |
| 199. C47 | #18696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20257788 | 2 |
| #20254766 | 2 |
| #20242536 | 2 |
| #20242474 | 2 |
| #20242126 | 2 |
| #20241840 | 2 |
| C47×#3131 | 2 |
| #18696 | 47 |