Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2286 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 2286 conjugacy classes of subgroups — too many to draw. Only its 360 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. C2×#16811568 | C2 | semidirect |
| 2. #20289891 | C2 | semidirect |
| 10. C22×C4×Dic53 | C4 | semidirect |
| 12. C2×C42×D53 | C4 | semidirect |
| 13. C2×C42×D53 | C4 | semidirect |
| 16. C22×C42×C53 | C4 | semidirect |
| 76. C42×C53 | C22⋊C4 | semidirect |
| 79. C4×Dic53 | C22⋊C4 | semidirect |
| 117. C22×C53 | #383 | semidirect |
| 124. C2×D53 | #383 | semidirect |
| 151. C22×C42 | #6157 | semidirect |
| 155. C53 | #14683 | semidirect |
| 218. C42 | C22⋊#6157 | semidirect |
| 262. C22 | #16811568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811568 | 2 |
| #20289891 | 2 |
| #20289889 | 2 |
| C22×C42×D53 | 2 |
| #14683 | 53 |