Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
226 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 9. #16810376 | C4 | semidirect |
| 13. C4×C16×C53 | C4 | semidirect |
| 102. C4×C16 | Dic53 | semidirect |
| 107. C53 | #7217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274843 | 2 |
| #20273474 | 2 |
| C53×#2162 | 2 |
| #7217 | 53 |