Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. #20273441 | C2 | semidirect |
| 3. #20272868 | C2 | semidirect |
| 4. C2×C53×#356 | C2 | semidirect |
| 15. #16810372 | C22 | semidirect |
| 19. C53×#356 | C22 | semidirect |
| 164. C2×#356 | D53 | semidirect |
| 184. #356 | C2×D53 | semidirect |
| 187. C53 | #13573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810805 | 2 |
| #20273441 | 2 |
| #20272868 | 2 |
| C2×C53×#356 | 2 |
| #13573 | 53 |