Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
202 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 60 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. #16811485 | C4 | semidirect |
| 13. C4×#11719908 | C4 | semidirect |
| 14. C4×C16×C53 | C4 | semidirect |
| 94. C4×C16 | #6157 | semidirect |
| 99. C53 | #7218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290637 | 2 |
| #20290278 | 2 |
| #20276512 | 2 |
| #7218 | 53 |