Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
156 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 27 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. Q82×C53 | C4 | semidirect |
| 9. C53×#333 | C4 | semidirect |
| 77. Q82 | Dic53 | semidirect |
| 82. #333 | Dic53 | semidirect |
| 84. C53 | #7520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272880 | 2 |
| #20272756 | 2 |
| C53×#1623 | 2 |
| #7520 | 53 |