Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
374 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 22. #13133292 | Q8 | semidirect |
| 143. C53 | #13290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290922 | 2 |
| #20290655 | 2 |
| #20289789 | 2 |
| #500×D53 | 2 |
| #13290 | 53 |