Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
982 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 199 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. #494×D53 | C2 | semidirect |
| 3. #486×D53 | C2 | semidirect |
| 4. #20274322 | C2 | semidirect |
| 5. #20274321 | C2 | semidirect |
| 6. #20274320 | C2 | semidirect |
| 7. #20274319 | C2 | semidirect |
| 8. C82×D53 | C2 | semidirect |
| 9. C53×#1709 | C2 | semidirect |
| 14. #16811003 | C22 | semidirect |
| 15. #16811002 | C22 | semidirect |
| 20. #16810971 | C22 | semidirect |
| 21. #16810970 | C22 | semidirect |
| 22. #16810969 | C22 | semidirect |
| 27. C8×#88322 | C22 | semidirect |
| 28. C8×#88322 | C22 | semidirect |
| 29. C53×#494 | C22 | semidirect |
| 31. C53×#486 | C22 | semidirect |
| 32. C82×C53 | C22 | semidirect |
| 149. #1709 | D53 | direct (N × H) |
| 155. D53 | #1709 | direct (N × H) |
| 163. #494 | C2×D53 | semidirect |
| 172. #486 | C2×D53 | semidirect |
| 178. C82 | C2×D53 | semidirect |
| 179. C53 | C2×#1709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #494×D53 | 2 |
| #493×D53 | 2 |
| #486×D53 | 2 |
| #20274322 | 2 |
| #20274321 | 2 |
| #20274320 | 2 |
| #20274319 | 2 |
| C82×D53 | 2 |
| C53×#1709 | 2 |
| C2×#1709 | 53 |