Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
262 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 88 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. #16811511 | C4 | semidirect |
| 13. C4⋊#11719908 | C4 | semidirect |
| 15. C53×C4⋊C16 | C4 | semidirect |
| 119. C4⋊C16 | #6157 | semidirect |
| 123. C53 | #7170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290916 | 2 |
| #20290509 | 2 |
| C4⋊C16×D53 | 2 |
| #7170 | 53 |