Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
560 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20252416 | C2 | semidirect |
| 3. C4×#13093940 | C2 | semidirect |
| 4. #20241987 | C2 | semidirect |
| 5. #20241985 | C2 | semidirect |
| 6. #20241252 | C2 | semidirect |
| 7. C47×#1288 | C2 | semidirect |
| 64. #13093935 | D4 | semidirect |
| 73. #97×C47 | D4 | semidirect |
| 237. #1288 | D47 | semidirect |
| 269. C47 | #9187 | semidirect |
| 309. #97 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252416 | 2 |
| #20249243 | 2 |
| C4×#13093940 | 2 |
| #20241987 | 2 |
| #20241985 | 2 |
| #20241252 | 2 |
| C47×#1288 | 2 |
| #9187 | 47 |