Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
842 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 250 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 |
|---|---|---|
| 7. C2×#13133271 | C4 | semidirect |
| 8. C2×C8×#6157 | C4 | semidirect |
| 9. #16811491 | C4 | semidirect |
| 11. #16810381 | C4 | semidirect |
| 12. C53×#338 | C4 | semidirect |
| 101. #338 | #6157 | semidirect |
| 103. C53 | #10699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811589 | 2 |
| #20290387 | 2 |
| #338×D53 | 2 |
| #10699 | 53 |