Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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. #13133209 | C8 | semidirect |
| 103. C53 | #7129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275696 | 2 |
| #20272544 | 2 |
| C53×#1274 | 2 |
| #7129 | 53 |