Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1638 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 1638 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 |
|---|---|---|
| 1. #20289902 | C2 | semidirect |
| 7. C2×#13133124 | C4 | semidirect |
| 8. #95×D53 | C4 | semidirect |
| 10. C2×#95×C53 | C4 | semidirect |
| 100. C2×#95 | #6157 | semidirect |
| 101. C53 | #14349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289902 | 2 |
| #20289889 | 2 |
| C2×#95×D53 | 2 |
| #14349 | 53 |