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. #20254391 | C2 | semidirect |
| 2. #20253762 | C2 | semidirect |
| 3. #20242102 | C2 | semidirect |
| 4. #20241986 | C2 | semidirect |
| 5. #20241899 | C2 | semidirect |
| 6. #20241281 | C2 | semidirect |
| 34. #13094024 | D4 | semidirect |
| 35. #13094024 | D4 | semidirect |
| 43. C4⋊(C47⋊C8) | D4 | semidirect |
| 52. #13093935 | D4 | semidirect |
| 231. C47 | #10096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254391 | 2 |
| #20253762 | 2 |
| #20242102 | 2 |
| #20241986 | 2 |
| #20241899 | 2 |
| #20241281 | 2 |
| C47×#2657 | 2 |
| #10096 | 47 |