Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 3. #20290930 | C2 | semidirect |
| 4. #20290524 | C2 | semidirect |
| 5. #20289787 | C2 | semidirect |
| 6. #20289781 | C2 | semidirect |
| 12. #16811664 | C4 | semidirect |
| 13. #16811664 | C4 | semidirect |
| 19. #16811535 | C4 | semidirect |
| 26. #16810437 | C4 | semidirect |
| 27. #16810436 | C4 | semidirect |
| 28. #16810435 | C4 | semidirect |
| 29. C53×#361 | C4 | semidirect |
| 42. D53⋊C16 | C2×C4 | semidirect |
| 43. #13133286 | C2×C4 | semidirect |
| 64. #13133157 | C2×C4 | semidirect |
| 67. #13133153 | C2×C4 | semidirect |
| 70. M32×C53 | C2×C4 | semidirect |
| 71. #108×C53 | C2×C4 | semidirect |
| 204. #361 | #6157 | semidirect |
| 209. C53 | #12647 | semidirect |
| 234. M32 | C2×#6157 | semidirect |
| 239. #108 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811664 | 2 |
| #20291024 | 2 |
| #20290930 | 2 |
| #20290524 | 2 |
| #20289787 | 2 |
| #20289781 | 2 |
| #361×D53 | 2 |
| #12647 | 53 |