Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 418 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. #20290894 | C2 | semidirect |
| 3. #20290249 | C2 | semidirect |
| 5. #20289579 | C2 | semidirect |
| 6. #20289565 | C2 | semidirect |
| 26. #16811032 | C4 | semidirect |
| 27. #16811029 | C4 | semidirect |
| 28. #16810982 | C4 | semidirect |
| 34. C53×#489 | C4 | semidirect |
| 217. #489 | #6157 | semidirect |
| 239. C53 | #9375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291652 | 2 |
| #20290894 | 2 |
| #20290249 | 2 |
| #20290116 | 2 |
| #20289579 | 2 |
| #20289565 | 2 |
| #20285932 | 2 |
| #9375 | 53 |