Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
728 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 163 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. #20254107 | C2 | semidirect |
| 3. #20253784 | C2 | semidirect |
| 4. #20243042 | C2 | semidirect |
| 5. #20243036 | C2 | semidirect |
| 6. #20243030 | C2 | semidirect |
| 7. #20243001 | C2 | semidirect |
| 8. #20241691 | C2 | semidirect |
| 9. C47×#3139 | C2 | semidirect |
| 158. #3139 | D47 | semidirect |
| 197. C47 | #19754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254126 | 2 |
| #20254107 | 2 |
| #20253784 | 2 |
| #20243042 | 2 |
| #20243036 | 2 |
| #20243030 | 2 |
| #20243001 | 2 |
| #20241691 | 2 |
| C47×#3139 | 2 |
| #19754 | 47 |