Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 74 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. #16811499 | C4 | semidirect |
| 12. C22⋊#11719908 | C4 | semidirect |
| 14. C53×C22⋊C16 | C4 | semidirect |
| 130. C22⋊C16 | #6157 | semidirect |
| 134. C53 | #7259 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290592 | 2 |
| #20290407 | 2 |
| C22⋊C16×D53 | 2 |
| #7259 | 53 |