Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1838 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1838 conjugacy classes of subgroups — too many to draw. Only its 251 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. C2×#16810999 | C2 | semidirect |
| 2. C2×#16810818 | C2 | semidirect |
| 3. #20273769 | C2 | direct (N × H) |
| 4. C2×#16810367 | C2 | semidirect |
| 5. C2×D4⋊#88322 | C2 | semidirect |
| 6. C2×D42×C53 | C2 | semidirect |
| 9. C2×#13133214 | C22 | semidirect |
| 11. #16810999 | C22 | semidirect |
| 13. #16810818 | C22 | semidirect |
| 14. C2×C4⋊#88322 | C22 | semidirect |
| 16. C2×C4×#88322 | C22 | semidirect |
| 17. #16810367 | C22 | semidirect |
| 18. D4⋊#88322 | C22 | semidirect |
| 22. D42×C53 | C22 | semidirect |
| 37. #13133214 | C23 | semidirect |
| 39. C4⋊#88322 | C23 | semidirect |
| 42. C4×#88322 | C23 | semidirect |
| 87. C2×D4×C53 | D8 | semidirect |
| 140. D4×C53 | C2×D8 | semidirect |
| 181. C2×D42 | D53 | semidirect |
| 189. C2×C53 | #1619 | semidirect |
| 198. D42 | C2×D53 | semidirect |
| 213. C53 | C2×#1619 | semidirect |
| 281. C2×D4 | #11719922 | semidirect |
| 332. D4 | C2×#11719922 | semidirect |
| 370. C2 | #20273769 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810999 | 2 |
| C2×#16810818 | 2 |
| #20273769 | 2 |
| C2×#16810367 | 2 |
| C2×D4⋊#88322 | 2 |
| C2×D42×C53 | 2 |
| C2×#1619 | 53 |