Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #20273188 | C2 | semidirect |
| 5. #20272576 | C2 | semidirect |
| 6. #20272546 | C2 | semidirect |
| 7. C53×#1531 | C2 | semidirect |
| 165. #1531 | D53 | semidirect |
| 196. C53 | #9285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285667 | 2 |
| #20283793 | 2 |
| #20273325 | 2 |
| #20273188 | 2 |
| #20272576 | 2 |
| #20272546 | 2 |
| C53×#1531 | 2 |
| #9285 | 53 |