Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20285453 | C2 | semidirect |
| 2. #20283626 | C2 | semidirect |
| 3. #20276930 | C2 | semidirect |
| 4. #20276887 | C2 | semidirect |
| 5. #20276792 | C2 | semidirect |
| 6. #20276663 | C2 | semidirect |
| 7. #20276615 | C2 | semidirect |
| 8. C53×#2165 | C2 | semidirect |
| 13. #16811021 | C22 | semidirect |
| 14. #16811000 | C22 | semidirect |
| 23. #16810736 | C22 | semidirect |
| 26. #16810446 | C22 | semidirect |
| 27. #16810437 | C22 | semidirect |
| 30. C53×#364 | C22 | semidirect |
| 32. C53×#347 | C22 | semidirect |
| 105. Dic212 | #41 | semidirect |
| 109. D424 | #41 | semidirect |
| 172. #2165 | D53 | semidirect |
| 197. #364 | C2×D53 | semidirect |
| 201. #347 | C2×D53 | semidirect |
| 202. C53 | #33688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285453 | 2 |
| #20283626 | 2 |
| #20276930 | 2 |
| #20276887 | 2 |
| #20276792 | 2 |
| #20276663 | 2 |
| #20276615 | 2 |
| C53×#2165 | 2 |
| #33688 | 53 |