Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 3. #20290471 | C2 | semidirect |
| 4. #20289815 | C2 | semidirect |
| 9. #16811533 | C4 | semidirect |
| 10. #16811531 | C4 | semidirect |
| 15. C2×#13133224 | C4 | semidirect |
| 19. #16810646 | C4 | semidirect |
| 21. C2×C8×Dic53 | C4 | semidirect |
| 22. C53×#408 | C4 | semidirect |
| 166. #408 | #6157 | semidirect |
| 174. C53 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291006 | 2 |
| #20290986 | 2 |
| #20290471 | 2 |
| #20289815 | 2 |
| #20283423 | 2 |
| #12633 | 53 |