Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
192 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 46 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. #16811516 | C4 | semidirect |
| 9. #16811464 | C4 | semidirect |
| 10. C8×#88324 | C4 | semidirect |
| 95. C53 | #7225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291085 | 2 |
| #20289938 | 2 |
| #20274862 | 2 |
| #7225 | 53 |