Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
222 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 222 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 |
|---|---|---|
| 24. #13133157 | C8 | semidirect |
| 32. M32×C53 | C8 | semidirect |
| 112. C53 | #7159 | semidirect |
| 120. M32 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290262 | 2 |
| C2×#16811486 | 2 |
| M32×Dic53 | 2 |
| #7159 | 53 |