Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
730 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 5. C2×C22⋊#88324 | C4 | semidirect |
| 26. C2×C22⋊Dic53 | C8 | semidirect |
| 33. C2×C22⋊C4×C53 | C8 | semidirect |
| 206. C53 | #7032 | semidirect |
| 225. C2×C22⋊C4 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290537 | 2 |
| #20272937 | 2 |
| #7032 | 53 |