Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
898 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 898 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 10. C2×#13133278 | C4 | semidirect |
| 227. C53 | #10940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133278 | 2 |
| #20291279 | 2 |
| C2×#16811504 | 2 |
| #20290421 | 2 |
| #20277300 | 2 |
| #10940 | 53 |