Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
502 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 155 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. C22×D848 | C2 | semidirect |
| 2. #20277027 | C2 | direct (N × H) |
| 3. C2×#16810460 | C2 | semidirect |
| 4. C2×#16810458 | C2 | semidirect |
| 5. C2×#16810457 | C2 | semidirect |
| 6. C2×C53×#508 | C2 | semidirect |
| 11. C2×D848 | C22 | semidirect |
| 12. #16810460 | C22 | semidirect |
| 13. #16810458 | C22 | semidirect |
| 14. #16810457 | C22 | semidirect |
| 15. C2×#13133123 | C22 | semidirect |
| 18. C53×#508 | C22 | semidirect |
| 19. C2×Q32×C53 | C22 | semidirect |
| 21. C2×D16×C53 | C22 | semidirect |
| 31. #13133123 | C23 | semidirect |
| 40. Q32×C53 | C23 | semidirect |
| 43. D16×C53 | C23 | semidirect |
| 110. C2×#508 | D53 | semidirect |
| 118. C2×C53 | #2263 | semidirect |
| 124. #508 | C2×D53 | semidirect |
| 125. C2×Q32 | C2×D53 | semidirect |
| 131. C2×D16 | C2×D53 | semidirect |
| 137. C53 | C2×#2263 | semidirect |
| 151. Q32 | C22×D53 | semidirect |
| 157. D16 | C22×D53 | semidirect |
| 227. C2 | #20277027 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| #20277027 | 2 |
| C2×#16810460 | 2 |
| C2×#16810458 | 2 |
| C2×#16810457 | 2 |
| C2×C53×#508 | 2 |
| C2×#2263 | 53 |