Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20275660 | C2 | semidirect |
| 4. C4×#13133150 | C2 | semidirect |
| 6. #20273005 | C2 | semidirect |
| 7. C53×#1503 | C2 | semidirect |
| 9. #16811019 | C4 | semidirect |
| 10. #16810997 | C4 | semidirect |
| 11. #16810973 | C4 | semidirect |
| 12. #16810971 | C4 | semidirect |
| 163. #88322 | #104 | semidirect |
| 189. #1503 | D53 | semidirect |
| 221. C53 | #9722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285275 | 2 |
| #20275660 | 2 |
| #20275633 | 2 |
| C4×#13133150 | 2 |
| #20273211 | 2 |
| #20273005 | 2 |
| C53×#1503 | 2 |
| #9722 | 53 |