Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
590 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20285843 | C2 | semidirect |
| 3. #20273400 | C2 | semidirect |
| 4. #20273209 | C2 | semidirect |
| 5. #20273106 | C2 | semidirect |
| 6. #20272618 | C2 | semidirect |
| 7. C53×#2563 | C2 | semidirect |
| 209. #2563 | D53 | semidirect |
| 244. C53 | #10241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285843 | 2 |
| #20284179 | 2 |
| #20273400 | 2 |
| #20273209 | 2 |
| #20273106 | 2 |
| #20272618 | 2 |
| C53×#2563 | 2 |
| #10241 | 53 |