Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 8. C4⋊#11719908 | C4 | semidirect |
| 12. C53×C4⋊C16 | C4 | semidirect |
| 50. C4×Dic53 | C16 | semidirect |
| 103. C4⋊C16 | Dic53 | semidirect |
| 108. C53 | #7148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276514 | 2 |
| C4×C8×Dic53 | 2 |
| C53×#2162 | 2 |
| #7148 | 53 |