Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20254393 | C2 | semidirect |
| 2. #20253763 | C2 | semidirect |
| 4. #20242101 | C2 | semidirect |
| 5. #20241985 | C2 | semidirect |
| 6. #20241899 | C2 | semidirect |
| 7. C47×#1300 | C2 | semidirect |
| 39. #13094024 | D4 | semidirect |
| 40. #13094024 | D4 | semidirect |
| 70. C4⋊C8×C47 | D4 | semidirect |
| 73. #97×C47 | D4 | semidirect |
| 201. #1300 | D47 | semidirect |
| 231. C47 | #10096 | semidirect |
| 265. C4⋊C8 | D188 | semidirect |
| 274. #97 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254393 | 2 |
| #20253763 | 2 |
| #20249494 | 2 |
| #20242101 | 2 |
| #20241985 | 2 |
| #20241899 | 2 |
| C47×#1300 | 2 |
| #10096 | 47 |