Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16810456 | C2 | semidirect |
| 3. M64×D53 | C2 | semidirect |
| 4. #20272858 | C2 | semidirect |
| 5. #20272857 | C2 | semidirect |
| 6. #20272856 | C2 | semidirect |
| 7. C53×#1401 | C2 | semidirect |
| 18. #16810457 | C22 | semidirect |
| 22. C2×#13133123 | C22 | semidirect |
| 25. C53×M64 | C22 | semidirect |
| 26. C2×C32×C53 | C22 | semidirect |
| 144. #1401 | D53 | semidirect |
| 166. M64 | C2×D53 | semidirect |
| 169. C2×C32 | C2×D53 | semidirect |
| 170. C53 | #13558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #504×D53 | 2 |
| C2×#16810456 | 2 |
| M64×D53 | 2 |
| #20272858 | 2 |
| #20272857 | 2 |
| #20272856 | 2 |
| C53×#1401 | 2 |
| #13558 | 53 |