Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3798 conjugacy classes of subgroups; only the 923 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 923 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. #20277891 | C2 | direct (N × H) |
| 3. C2×#16810501 | C2 | semidirect |
| 4. C2×#16810491 | C2 | semidirect |
| 5. C2×C53×#383 | C2 | semidirect |
| 8. C2×#13133214 | C4 | semidirect |
| 11. #16810501 | C22 | semidirect |
| 12. #16810491 | C22 | semidirect |
| 15. C53×#383 | C22 | semidirect |
| 20. C22×D212 | C2×C4 | semidirect |
| 25. #13133214 | C2×C4 | semidirect |
| 31. C2×C42×C53 | C2×C4 | semidirect |
| 49. C2×D212 | C22×C4 | semidirect |
| 52. C42×C53 | C22×C4 | semidirect |
| 88. C2×#383 | D53 | semidirect |
| 89. C2×C53 | #2380 | semidirect |
| 101. #383 | C2×D53 | semidirect |
| 104. C53 | C2×#2380 | semidirect |
| 118. C2×C42 | C4×D53 | semidirect |
| 141. C42 | C2×C4×D53 | semidirect |
| 172. C2 | #20277891 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133214 | 2 |
| #20277891 | 2 |
| C2×#16810501 | 2 |
| C2×#16810491 | 2 |
| C2×C53×#383 | 2 |
| C2×#2380 | 53 |