Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
640 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #20283196 | C2 | semidirect |
| 3. #20276365 | C2 | semidirect |
| 4. #20274691 | C2 | semidirect |
| 5. #20272845 | C2 | semidirect |
| 6. #20272837 | C2 | semidirect |
| 7. C53×#2134 | C2 | semidirect |
| 9. C2×#13133243 | C4 | semidirect |
| 10. C22×#11719923 | C4 | semidirect |
| 18. #16810631 | C4 | semidirect |
| 19. #16810617 | C4 | semidirect |
| 241. #2134 | D53 | semidirect |
| 276. C53 | #13098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283999 | 2 |
| #20283196 | 2 |
| #20276365 | 2 |
| #20274691 | 2 |
| #20272845 | 2 |
| #20272837 | 2 |
| C53×#2134 | 2 |
| #13098 | 53 |