Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
326 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #20272890 | C2 | semidirect |
| 11. C53×#533 | C4 | semidirect |
| 13. C53×#488 | C4 | semidirect |
| 19. C2×C4×C8×C53 | C4 | semidirect |
| 137. #533 | Dic53 | semidirect |
| 139. #488 | Dic53 | semidirect |
| 147. C2×C4×C8 | Dic53 | semidirect |
| 152. C53 | #13602 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276400 | 2 |
| #20276380 | 2 |
| #20272890 | 2 |
| C53×#3131 | 2 |
| #13602 | 53 |