Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
658 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 8. #16811491 | C4 | semidirect |
| 13. C2×#13133128 | C4 | semidirect |
| 14. C2×#13133127 | C4 | semidirect |
| 15. C2×C8×Dic53 | C4 | semidirect |
| 16. C2×C4×C8×C53 | C4 | semidirect |
| 145. C2×C4×C8 | #6157 | semidirect |
| 149. C53 | #10814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290414 | 2 |
| #20290401 | 2 |
| C2×#16811491 | 2 |
| C2×#16810577 | 2 |
| #10814 | 53 |