Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
430 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 76 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. #20290893 | C2 | semidirect |
| 3. #20290245 | C2 | semidirect |
| 5. #20289579 | C2 | semidirect |
| 6. #20289565 | C2 | semidirect |
| 26. #16811018 | C4 | semidirect |
| 27. #16810992 | C4 | semidirect |
| 28. #16810991 | C4 | semidirect |
| 34. C53×#497 | C4 | semidirect |
| 220. #497 | #6157 | semidirect |
| 244. C53 | #9376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291652 | 2 |
| #20290893 | 2 |
| #20290245 | 2 |
| #20290116 | 2 |
| #20289579 | 2 |
| #20289565 | 2 |
| #20285738 | 2 |
| #9376 | 53 |