Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20287853 | C2 | semidirect |
| 2. #20286515 | C2 | semidirect |
| 3. #20276965 | C2 | semidirect |
| 4. #20276836 | C2 | semidirect |
| 5. #20276791 | C2 | semidirect |
| 6. #20276673 | C2 | semidirect |
| 7. #20276553 | C2 | semidirect |
| 8. C53×#2178 | C2 | semidirect |
| 10. #16811425 | C22 | semidirect |
| 12. #16811058 | C22 | semidirect |
| 14. C2×D848 | C22 | semidirect |
| 15. C2×D848 | C22 | semidirect |
| 17. #16811039 | C22 | semidirect |
| 18. #16811000 | C22 | semidirect |
| 19. #16810894 | C22 | semidirect |
| 23. #16810444 | C22 | semidirect |
| 24. #16810435 | C22 | semidirect |
| 25. #16810406 | C22 | semidirect |
| 27. C53×#443 | C22 | semidirect |
| 28. C53×#368 | C22 | semidirect |
| 29. C53×#359 | C22 | semidirect |
| 30. C4×C16×C53 | C22 | semidirect |
| 58. Q32×C53 | D4 | semidirect |
| 59. SD32×C53 | D4 | semidirect |
| 60. D16×C53 | D4 | semidirect |
| 144. #2178 | D53 | semidirect |
| 166. #443 | C2×D53 | semidirect |
| 167. #368 | C2×D53 | semidirect |
| 170. #359 | C2×D53 | semidirect |
| 172. C4×C16 | C2×D53 | semidirect |
| 173. C53 | #33858 | semidirect |
| 190. Q32 | D212 | semidirect |
| 192. SD32 | D212 | semidirect |
| 197. D16 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287853 | 2 |
| #20286515 | 2 |
| #20276965 | 2 |
| #20276836 | 2 |
| #20276791 | 2 |
| #20276673 | 2 |
| #20276553 | 2 |
| C53×#2178 | 2 |
| #33858 | 53 |