Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
272 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 272 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 |
|---|---|---|
| 19. C53×#367 | C4 | semidirect |
| 20. C53×#366 | C4 | semidirect |
| 138. #367 | Dic53 | semidirect |
| 139. #366 | Dic53 | semidirect |
| 142. C53 | #13118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275454 | 2 |
| #20274601 | 2 |
| #20272823 | 2 |
| #20272820 | 2 |
| #20272814 | 2 |
| #20272794 | 2 |
| C53×#2159 | 2 |
| #13118 | 53 |