Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
374 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 103 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×#13133153 | C4 | semidirect |
| 13. C53×C22⋊C16 | C4 | semidirect |
| 128. C22⋊C16 | Dic53 | semidirect |
| 132. C53 | #7264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274753 | 2 |
| C2×#16810386 | 2 |
| C53×#2112 | 2 |
| #7264 | 53 |