Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1140 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1140 conjugacy classes of subgroups — too many to draw. Only its 175 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. #20282997 | C2 | semidirect |
| 2. #20276141 | C2 | semidirect |
| 3. #20275897 | C2 | semidirect |
| 4. #20275894 | C2 | semidirect |
| 5. #20275711 | C2 | semidirect |
| 6. #20274625 | C2 | semidirect |
| 7. C53×#2847 | C2 | semidirect |
| 8. C22×#11719922 | C22 | semidirect |
| 11. C2×#13133150 | C22 | semidirect |
| 12. C2×#13133138 | C22 | semidirect |
| 13. C2×#13133137 | C22 | semidirect |
| 18. #16810385 | C22 | semidirect |
| 19. #16810385 | C22 | semidirect |
| 59. C24×C53 | D8 | semidirect |
| 165. #2847 | D53 | semidirect |
| 194. C53 | #32706 | semidirect |
| 230. C24 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282997 | 2 |
| #20276141 | 2 |
| #20275897 | 2 |
| #20275894 | 2 |
| #20275711 | 2 |
| #20274625 | 2 |
| C53×#2847 | 2 |
| #32706 | 53 |