Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
582 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 2. #20290451 | C2 | semidirect |
| 4. #20289557 | C2 | semidirect |
| 12. #16811469 | C4 | semidirect |
| 13. #16811466 | C4 | semidirect |
| 14. C23×#88322 | C4 | semidirect |
| 19. C2×#13133146 | C4 | semidirect |
| 21. C2×C8×Dic53 | C4 | semidirect |
| 22. C2×C22⋊C8×C53 | C4 | semidirect |
| 103. C23×C53 | #97 | semidirect |
| 128. C2×Dic53 | #97 | semidirect |
| 138. #88322 | #99 | semidirect |
| 184. C2×C22⋊C8 | #6157 | semidirect |
| 192. C53 | #8160 | semidirect |
| 278. C23 | #13133271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133275 | 2 |
| #20290451 | 2 |
| #20289950 | 2 |
| #20289557 | 2 |
| C2×#16810686 | 2 |
| #8160 | 53 |