Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1062 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1062 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. #20283002 | C2 | semidirect |
| 2. #20276151 | C2 | semidirect |
| 3. #20275911 | C2 | semidirect |
| 4. #20275901 | C2 | semidirect |
| 5. #20275718 | C2 | semidirect |
| 6. #20274625 | C2 | semidirect |
| 8. C22×#11719923 | C22 | semidirect |
| 10. C2×#13133148 | C22 | semidirect |
| 11. C2×#13133140 | C22 | semidirect |
| 12. C2×#13133138 | C22 | semidirect |
| 18. #16810385 | C22 | semidirect |
| 19. #16810385 | C22 | semidirect |
| 58. C24×C53 | SD16 | semidirect |
| 184. C53 | #32708 | semidirect |
| 218. C24 | #11719923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283002 | 2 |
| #20276151 | 2 |
| #20275911 | 2 |
| #20275901 | 2 |
| #20275718 | 2 |
| #20274625 | 2 |
| C53×#2847 | 2 |
| #32708 | 53 |