Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1462 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 1462 conjugacy classes of subgroups — too many to draw. Only its 272 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×#13133217 | C4 | semidirect |
| 11. C2×#13133216 | C4 | semidirect |
| 12. C2×#13133215 | C4 | semidirect |
| 16. C2×C4⋊Q8×C53 | C4 | semidirect |
| 122. C2×C4⋊Q8 | #6157 | semidirect |
| 129. C53 | #14663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811568 | 2 |
| #20289905 | 2 |
| #20289904 | 2 |
| C2×C4⋊Q8×D53 | 2 |
| #14663 | 53 |