Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 13. C53×#424 | C4 | semidirect |
| 14. C53×#424 | C4 | semidirect |
| 17. C4×M16×C53 | C4 | semidirect |
| 18. C2×C4×C8×C53 | C4 | semidirect |
| 126. #424 | Dic53 | semidirect |
| 127. #424 | Dic53 | semidirect |
| 132. C4×M16 | Dic53 | semidirect |
| 133. C2×C4×C8 | Dic53 | semidirect |
| 136. C53 | #12864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274819 | 2 |
| #20272844 | 2 |
| #20272838 | 2 |
| #20272836 | 2 |
| C53×#2922 | 2 |
| #12864 | 53 |