Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
352 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 5. C2×#13133149 | C4 | semidirect |
| 8. C22⋊#11719908 | C4 | semidirect |
| 13. C53×#340 | C4 | semidirect |
| 128. #340 | Dic53 | semidirect |
| 129. C53 | #7262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276326 | 2 |
| #20274740 | 2 |
| C53×#1735 | 2 |
| #7262 | 53 |