Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
446 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. #20242179 | C2 | semidirect |
| 3. #20242121 | C2 | semidirect |
| 4. #20242056 | C2 | semidirect |
| 5. #20241806 | C2 | semidirect |
| 6. #20241278 | C2 | semidirect |
| 7. C47×#1965 | C2 | semidirect |
| 168. #1965 | D47 | semidirect |
| 199. C47 | #10488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254306 | 2 |
| #20242179 | 2 |
| #20242121 | 2 |
| #20242056 | 2 |
| #20241806 | 2 |
| #20241278 | 2 |
| C47×#1965 | 2 |
| #10488 | 47 |