Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 91 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. C22⋊C16×D53 | C2 | semidirect |
| 3. #341×D53 | C2 | semidirect |
| 4. #20272731 | C2 | semidirect |
| 5. #20272730 | C2 | semidirect |
| 6. #20272729 | C2 | semidirect |
| 7. C53×#1349 | C2 | semidirect |
| 20. C22⋊#11719908 | C22 | semidirect |
| 22. #16810388 | C22 | semidirect |
| 25. C53×C22⋊C16 | C22 | semidirect |
| 26. C53×#341 | C22 | semidirect |
| 190. #1349 | D53 | direct (N × H) |
| 198. D53 | #1349 | direct (N × H) |
| 214. C22⋊C16 | C2×D53 | semidirect |
| 217. #341 | C2×D53 | semidirect |
| 218. C53 | C2×#1349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #466×D53 | 2 |
| C22⋊C16×D53 | 2 |
| #341×D53 | 2 |
| #20272731 | 2 |
| #20272730 | 2 |
| #20272729 | 2 |
| C53×#1349 | 2 |
| C2×#1349 | 53 |