Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
674 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
|---|---|---|
| 21. #16811021 | C4 | semidirect |
| 22. #16811020 | C4 | semidirect |
| 23. #16811019 | C4 | semidirect |
| 26. C53×#498 | C4 | semidirect |
| 139. #498 | #6157 | semidirect |
| 154. C53 | #22253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291210 | 2 |
| #20290899 | 2 |
| #20290778 | 2 |
| #20290777 | 2 |
| #20290637 | 2 |
| #20290433 | 2 |
| #498×D53 | 2 |
| #22253 | 53 |