Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 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. #20283631 | C2 | semidirect |
| 3. C2×#16810429 | C2 | semidirect |
| 4. #20276420 | C2 | semidirect |
| 5. #20275611 | C2 | semidirect |
| 6. #20272805 | C2 | semidirect |
| 7. C53×#1389 | C2 | semidirect |
| 12. #16811066 | C4 | semidirect |
| 14. #16811061 | C4 | semidirect |
| 180. #1389 | D53 | semidirect |
| 209. C53 | #13021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287851 | 2 |
| #20283631 | 2 |
| C2×#16810429 | 2 |
| #20276420 | 2 |
| #20275611 | 2 |
| #20272805 | 2 |
| C53×#1389 | 2 |
| #13021 | 53 |