Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
684 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20254391 | C2 | semidirect |
| 2. #20253763 | C2 | semidirect |
| 4. #20242101 | C2 | semidirect |
| 5. #20241901 | C2 | semidirect |
| 6. #20241282 | C2 | semidirect |
| 7. C47×#1527 | C2 | semidirect |
| 37. #13094024 | D4 | semidirect |
| 38. #13094024 | D4 | semidirect |
| 53. C4⋊(C47⋊C8) | D4 | semidirect |
| 75. #97×C47 | D4 | semidirect |
| 199. #1527 | D47 | semidirect |
| 231. C47 | #10096 | semidirect |
| 274. #97 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254391 | 2 |
| #20253763 | 2 |
| #20249496 | 2 |
| #20242101 | 2 |
| #20241901 | 2 |
| #20241282 | 2 |
| C47×#1527 | 2 |
| #10096 | 47 |