Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
174 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 174 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. C53×#430 | C4 | semidirect |
| 10. C53×H(3,ℤ/4) | C4 | semidirect |
| 81. #430 | Dic53 | semidirect |
| 87. H(3,ℤ/4) | Dic53 | semidirect |
| 88. C53 | #7438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272836 | 2 |
| #20272641 | 2 |
| C53×#2098 | 2 |
| #7438 | 53 |