Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. #20287848 | C2 | semidirect |
| 2. #20277028 | C2 | semidirect |
| 3. #20276815 | C2 | semidirect |
| 4. #20272903 | C2 | semidirect |
| 5. #20272902 | C2 | semidirect |
| 6. #20272854 | C2 | semidirect |
| 7. C53×#2263 | C2 | semidirect |
| 19. #16810457 | C22 | semidirect |
| 20. #16810451 | C22 | semidirect |
| 23. C2×D16×C53 | C22 | semidirect |
| 26. C53×M64 | C22 | semidirect |
| 38. Dic424 | D4 | semidirect |
| 43. D848 | D4 | semidirect |
| 53. Q32×C53 | D4 | semidirect |
| 57. D16×C53 | D4 | semidirect |
| 141. #2263 | D53 | semidirect |
| 160. C2×D16 | C2×D53 | semidirect |
| 168. M64 | C2×D53 | semidirect |
| 171. C53 | #13667 | semidirect |
| 187. Q32 | C22⋊D53 | semidirect |
| 196. D16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287848 | 2 |
| #20277028 | 2 |
| #20276815 | 2 |
| #20272903 | 2 |
| #20272902 | 2 |
| #20272854 | 2 |
| C53×#2263 | 2 |
| #13667 | 53 |