Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
688 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20283176 | C2 | semidirect |
| 3. #20276386 | C2 | semidirect |
| 4. #20276366 | C2 | semidirect |
| 5. #20272845 | C2 | semidirect |
| 6. #20272835 | C2 | semidirect |
| 7. C53×#1795 | C2 | semidirect |
| 8. C2×#13133242 | C4 | semidirect |
| 9. C22×#11719922 | C4 | semidirect |
| 16. #16810628 | C4 | semidirect |
| 17. #16810619 | C4 | semidirect |
| 31. C22×D212 | C2×C4 | semidirect |
| 38. C2×#11719917 | C2×C4 | semidirect |
| 39. C22×#88322 | C2×C4 | semidirect |
| 50. #13133176 | C2×C4 | semidirect |
| 254. #1795 | D53 | semidirect |
| 289. C53 | #13102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283983 | 2 |
| #20283176 | 2 |
| #20276386 | 2 |
| #20276366 | 2 |
| #20272845 | 2 |
| #20272835 | 2 |
| C53×#1795 | 2 |
| #13102 | 53 |