Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
166 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 6. C2×#106×C53 | C4 | semidirect |
| 10. C53×#341 | C4 | semidirect |
| 82. C2×#106 | Dic53 | semidirect |
| 88. #341 | Dic53 | semidirect |
| 89. C53 | #7410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272836 | 2 |
| #20272653 | 2 |
| C53×#2079 | 2 |
| #7410 | 53 |