Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
392 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20273482 | C2 | semidirect |
| 4. #20272609 | C2 | semidirect |
| 19. C53×#329 | C4 | semidirect |
| 20. C53×#329 | C4 | semidirect |
| 21. C53×#329 | C4 | semidirect |
| 156. #329 | Dic53 | semidirect |
| 157. #329 | Dic53 | semidirect |
| 158. #329 | Dic53 | semidirect |
| 159. C53 | #8918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283786 | 2 |
| #20275548 | 2 |
| #20273482 | 2 |
| #20272609 | 2 |
| C53×#1525 | 2 |
| #8918 | 53 |