Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1630 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 352 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. #20289895 | C2 | semidirect |
| 8. #16811565 | C4 | semidirect |
| 14. #16810486 | C4 | semidirect |
| 15. #16810485 | C4 | semidirect |
| 16. #16810484 | C4 | semidirect |
| 18. C53×#381 | C4 | semidirect |
| 60. C22×C4×C53 | C42 | semidirect |
| 64. C22×Dic53 | C42 | semidirect |
| 74. C2×C4×D53 | C42 | semidirect |
| 167. #381 | #6157 | semidirect |
| 173. C53 | #13828 | semidirect |
| 229. C22×C4 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811565 | 2 |
| #20289896 | 2 |
| #20289895 | 2 |
| #381×D53 | 2 |
| #13828 | 53 |