Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 26. #16810915 | C4 | semidirect |
| 27. #16810909 | C4 | semidirect |
| 28. #16810908 | C4 | semidirect |
| 32. C53×#477 | C4 | semidirect |
| 209. #477 | #6157 | semidirect |
| 229. C53 | #9308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291612 | 2 |
| #20290586 | 2 |
| #20290147 | 2 |
| #20290024 | 2 |
| #20289605 | 2 |
| #20289570 | 2 |
| #20284521 | 2 |
| #9308 | 53 |