Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
222 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 27. #107×C53 | C8 | semidirect |
| 111. C53 | #7121 | semidirect |
| 124. #107 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289754 | 2 |
| #20289545 | 2 |
| #20275449 | 2 |
| #7121 | 53 |