Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
468 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#16810418 | C2 | semidirect |
| 3. #20272873 | C2 | direct (N × H) |
| 4. C2×C53×#355 | C2 | semidirect |
| 7. C2×#13133214 | C4 | semidirect |
| 10. #16811013 | C4 | semidirect |
| 13. C2×#13133128 | C4 | semidirect |
| 15. #16810418 | C22 | semidirect |
| 19. C53×#355 | C22 | semidirect |
| 33. #13133214 | C2×C4 | semidirect |
| 38. #13133128 | C2×C4 | semidirect |
| 155. C2×#355 | D53 | semidirect |
| 162. C2×C53 | #1406 | semidirect |
| 177. #355 | C2×D53 | semidirect |
| 180. C53 | C2×#1406 | semidirect |
| 319. C2 | #20272873 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811013 | 2 |
| C2×#16810418 | 2 |
| #20272873 | 2 |
| C2×C53×#355 | 2 |
| C2×#1406 | 53 |