Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
262 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 98 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. #16811509 | C4 | semidirect |
| 9. #16811484 | C4 | semidirect |
| 26. #13133149 | C8 | semidirect |
| 35. #106×C53 | C8 | semidirect |
| 123. C53 | #7174 | semidirect |
| 136. #106 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290921 | 2 |
| #20290262 | 2 |
| #106×Dic53 | 2 |
| #7174 | 53 |