Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 81 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. M64×D53 | C2 | semidirect |
| 3. #367×D53 | C2 | semidirect |
| 4. #20272903 | C2 | semidirect |
| 5. #20272902 | C2 | semidirect |
| 6. #20272901 | C2 | semidirect |
| 7. C53×#1418 | C2 | semidirect |
| 9. #16811056 | C4 | semidirect |
| 13. #16811052 | C4 | semidirect |
| 14. Q32×D53 | C4 | semidirect |
| 16. D16×D53 | C4 | semidirect |
| 19. #16810457 | C22 | semidirect |
| 22. #16810451 | C22 | semidirect |
| 25. C53×M64 | C22 | semidirect |
| 26. C53×#367 | C22 | semidirect |
| 38. Dic424 | C2×C4 | semidirect |
| 43. D848 | C2×C4 | semidirect |
| 54. Q32×C53 | C2×C4 | semidirect |
| 56. D16×C53 | C2×C4 | semidirect |
| 147. #1418 | D53 | direct (N × H) |
| 153. D53 | #1418 | direct (N × H) |
| 168. M64 | C2×D53 | semidirect |
| 172. #367 | C2×D53 | semidirect |
| 173. C53 | C2×#1418 | semidirect |
| 188. Q32 | C4×D53 | semidirect |
| 195. D16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D53 | 2 |
| M64×D53 | 2 |
| #367×D53 | 2 |
| #20272903 | 2 |
| #20272902 | 2 |
| #20272901 | 2 |
| C53×#1418 | 2 |
| C2×#1418 | 53 |