Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20290890 | C2 | semidirect |
| 4. #20290025 | C2 | semidirect |
| 5. #20289550 | C2 | semidirect |
| 6. #20289547 | C2 | semidirect |
| 24. #16811019 | C4 | semidirect |
| 25. #16810997 | C4 | semidirect |
| 26. #16810970 | C4 | semidirect |
| 30. C53×#487 | C4 | semidirect |
| 105. #11719936 | SD16 | semidirect |
| 211. #487 | #6157 | semidirect |
| 229. C53 | #9055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291461 | 2 |
| #20290890 | 2 |
| #20290096 | 2 |
| #20290025 | 2 |
| #20289550 | 2 |
| #20289547 | 2 |
| #20285277 | 2 |
| #9055 | 53 |