Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3294 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 627 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 |
|---|---|---|
| 1. #20282980 | C2 | direct (N × H) |
| 2. C2×#16810559 | C2 | semidirect |
| 3. C2×#16810547 | C2 | semidirect |
| 4. C2×#16810545 | C2 | semidirect |
| 6. C2×C53×#399 | C2 | semidirect |
| 8. C22×C4⋊Dic53 | C22 | semidirect |
| 9. C22×#11719919 | C22 | semidirect |
| 13. #16810559 | C22 | semidirect |
| 14. #16810547 | C22 | semidirect |
| 15. #16810545 | C22 | semidirect |
| 17. C2×#13133124 | C22 | semidirect |
| 18. C22×C4⋊C4×C53 | C22 | semidirect |
| 20. C53×#399 | C22 | semidirect |
| 21. C2×#95×C53 | C22 | semidirect |
| 29. C2×C4⋊Dic53 | C23 | semidirect |
| 31. C2×#11719919 | C23 | semidirect |
| 38. #13133124 | C23 | semidirect |
| 43. C2×C4⋊C4×C53 | C23 | semidirect |
| 46. #95×C53 | C23 | semidirect |
| 130. C2×#399 | D53 | semidirect |
| 135. C2×C53 | #2842 | semidirect |
| 143. C22×C4⋊C4 | C2×D53 | semidirect |
| 149. #399 | C2×D53 | semidirect |
| 154. C2×#95 | C2×D53 | semidirect |
| 155. C53 | C2×#2842 | semidirect |
| 170. C2×C4⋊C4 | C22×D53 | semidirect |
| 180. #95 | C22×D53 | semidirect |
| 263. C2 | #20282980 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282980 | 2 |
| C2×#16810559 | 2 |
| C2×#16810547 | 2 |
| C2×#16810545 | 2 |
| C2×#16810478 | 2 |
| C2×C53×#399 | 2 |
| C2×#2842 | 53 |