Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1116 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 1. #20289115 | C2 | semidirect |
| 2. #20285165 | C2 | semidirect |
| 3. #20274007 | C2 | semidirect |
| 4. #20273310 | C2 | semidirect |
| 5. #20273306 | C2 | semidirect |
| 6. C53×#3138 | C2 | semidirect |
| 8. #16811371 | C22 | semidirect |
| 19. #16810365 | C22 | semidirect |
| 20. #16810362 | C22 | semidirect |
| 153. #3138 | D53 | semidirect |
| 182. C53 | #19075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289115 | 2 |
| #20285165 | 2 |
| #20274007 | 2 |
| #20273310 | 2 |
| #20273306 | 2 |
| C53×#3138 | 2 |
| #19075 | 53 |