Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
728 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20254106 | C2 | semidirect |
| 3. #20253782 | C2 | semidirect |
| 4. #20253769 | C2 | semidirect |
| 5. #20243041 | C2 | semidirect |
| 6. #20243034 | C2 | semidirect |
| 7. #20243027 | C2 | semidirect |
| 8. #20243000 | C2 | semidirect |
| 9. C47×#1455 | C2 | semidirect |
| 163. #1455 | 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 |
| #20254106 | 2 |
| #20253782 | 2 |
| #20253769 | 2 |
| #20243041 | 2 |
| #20243034 | 2 |
| #20243027 | 2 |
| #20243000 | 2 |
| C47×#1455 | 2 |
| #19754 | 47 |