Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
508 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20244999 | C2 | semidirect |
| 2. #20243105 | C2 | semidirect |
| 3. #20241397 | C2 | semidirect |
| 8. C22⋊(C47⋊C16) | C22 | semidirect |
| 10. #15688886 | C22 | semidirect |
| 11. C22×D8×C47 | C4 | semidirect |
| 16. C47×#466 | C4 | semidirect |
| 18. C2×#107×C47 | C4 | semidirect |
| 161. C22×D8 | Dic47 | semidirect |
| 168. #466 | Dic47 | semidirect |
| 170. C2×#107 | Dic47 | semidirect |
| 176. C47 | #11705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244999 | 2 |
| #20243105 | 2 |
| #20241397 | 2 |
| C2×C47×#466 | 2 |
| #11705 | 47 |