Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
394 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 115 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. C4×#13133151 | C2 | semidirect |
| 3. #20272725 | C2 | semidirect |
| 4. C53×#2162 | C2 | semidirect |
| 6. #16811028 | C4 | semidirect |
| 7. #16811000 | C4 | semidirect |
| 12. C4×D424 | C4 | semidirect |
| 126. #2162 | D53 | semidirect |
| 150. C53 | #11742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285294 | 2 |
| C4×#13133151 | 2 |
| #20272725 | 2 |
| C53×#2162 | 2 |
| #11742 | 53 |