Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20273478 | C2 | semidirect |
| 3. #20272759 | C2 | semidirect |
| 4. C53×#2162 | C2 | semidirect |
| 15. #16810374 | C22 | semidirect |
| 17. C53×C4⋊C16 | C22 | semidirect |
| 129. #2162 | D53 | semidirect |
| 147. C4⋊C16 | C2×D53 | semidirect |
| 152. C53 | #11957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811007 | 2 |
| #20273478 | 2 |
| #20272759 | 2 |
| C53×#2162 | 2 |
| #11957 | 53 |