Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
286 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. C2×#13133157 | C4 | semidirect |
| 14. C53×C22⋊C16 | C4 | semidirect |
| 125. C22⋊C16 | Dic53 | semidirect |
| 127. C53 | #7201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276326 | 2 |
| #20274491 | 2 |
| C53×#2112 | 2 |
| #7201 | 53 |