Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
392 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 74 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. #20290281 | C2 | semidirect |
| 4. #20290280 | C2 | semidirect |
| 5. #20289604 | C2 | semidirect |
| 6. #20289604 | C2 | semidirect |
| 27. #16810363 | C4 | semidirect |
| 28. #16810362 | C4 | semidirect |
| 29. #16810362 | C4 | semidirect |
| 30. C53×#329 | C4 | semidirect |
| 216. #329 | #6157 | semidirect |
| 217. C53 | #8918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291601 | 2 |
| #20290852 | 2 |
| #20290281 | 2 |
| #20290280 | 2 |
| #20289604 | 2 |
| #20273305 | 2 |
| #8918 | 53 |