Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #20274881 | C2 | semidirect |
| 5. #20272597 | C2 | semidirect |
| 6. #20272596 | C2 | semidirect |
| 7. C53×#1847 | C2 | semidirect |
| 22. #16810362 | C4 | semidirect |
| 53. #13133128 | C2×C4 | semidirect |
| 68. #97×C53 | C2×C4 | semidirect |
| 200. #1847 | D53 | semidirect |
| 232. C53 | #8910 | semidirect |
| 269. #97 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277886 | 2 |
| #20275529 | 2 |
| #20274881 | 2 |
| C2×#16810362 | 2 |
| #20272597 | 2 |
| #20272596 | 2 |
| C53×#1847 | 2 |
| #8910 | 53 |