Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
444 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 25. #16810909 | C4 | semidirect |
| 26. #16810908 | C4 | semidirect |
| 27. #16810830 | C4 | semidirect |
| 32. C53×#462 | C4 | semidirect |
| 215. #462 | #6157 | semidirect |
| 234. C53 | #9328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291199 | 2 |
| #20290891 | 2 |
| #20290107 | 2 |
| #20290058 | 2 |
| #20289602 | 2 |
| #20289567 | 2 |
| #20284844 | 2 |
| #9328 | 53 |