Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
820 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20275546 | C2 | semidirect |
| 3. #20273435 | C2 | semidirect |
| 4. #20273349 | C2 | semidirect |
| 5. #20273224 | C2 | semidirect |
| 6. #20273223 | C2 | semidirect |
| 7. C53×#1557 | C2 | semidirect |
| 11. #16811338 | C4 | semidirect |
| 13. D4×D212 | C4 | semidirect |
| 20. #16810680 | C22 | semidirect |
| 22. #16810469 | C22 | semidirect |
| 29. C53×#432 | C22 | semidirect |
| 30. C53×#423 | C22 | semidirect |
| 230. #1557 | D53 | semidirect |
| 255. #432 | C2×D53 | semidirect |
| 256. #423 | C2×D53 | semidirect |
| 266. C53 | #8491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289120 | 2 |
| #20275546 | 2 |
| #20273435 | 2 |
| #20273349 | 2 |
| #20273224 | 2 |
| #20273223 | 2 |
| C53×#1557 | 2 |
| #8491 | 53 |