Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
246 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
| 14. C4×C16×C53 | C4 | semidirect |
| 48. C4×Dic53 | C16 | semidirect |
| 103. C4×C16 | Dic53 | semidirect |
| 106. C53 | #7142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276514 | 2 |
| #20274460 | 2 |
| C53×#2162 | 2 |
| #7142 | 53 |