Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 13. #16810399 | C4 | semidirect |
| 14. #16810398 | C4 | semidirect |
| 15. C53×#346 | C4 | semidirect |
| 110. #346 | #6157 | semidirect |
| 111. C53 | #12890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290652 | 2 |
| #20290651 | 2 |
| #20289773 | 2 |
| #346×D53 | 2 |
| #12890 | 53 |