Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
222 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 17. C2×#11719908 | C8 | semidirect |
| 23. C2×C16×C53 | C8 | semidirect |
| 81. C53 | #7155 | semidirect |
| 90. C2×C16 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290262 | 2 |
| C2×C16×Dic53 | 2 |
| #7155 | 53 |