Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 3. #20290139 | C2 | semidirect |
| 4. #20290039 | C2 | semidirect |
| 5. #20289576 | C2 | semidirect |
| 6. #20289571 | C2 | semidirect |
| 26. #16811033 | C4 | semidirect |
| 27. #16810985 | C4 | semidirect |
| 28. #16810983 | C4 | semidirect |
| 34. C53×#501 | C4 | semidirect |
| 200. #501 | #6157 | semidirect |
| 224. C53 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291539 | 2 |
| #20290158 | 2 |
| #20290139 | 2 |
| #20290039 | 2 |
| #20289576 | 2 |
| #20289571 | 2 |
| #20285956 | 2 |
| #9369 | 53 |