Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
230 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 82 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. #16811544 | C4 | semidirect |
| 9. #16811485 | C4 | semidirect |
| 122. C53 | #7279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291049 | 2 |
| #20290264 | 2 |
| #20274876 | 2 |
| #7279 | 53 |