Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
410 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 126 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. #20290927 | C2 | semidirect |
| 4. #20289767 | C2 | semidirect |
| 8. C2×#13133292 | C4 | semidirect |
| 10. C2×#13133291 | C4 | semidirect |
| 11. C2×D53⋊C16 | C4 | semidirect |
| 13. C22×#11719910 | C4 | semidirect |
| 22. #16810405 | C4 | semidirect |
| 23. #16810404 | C4 | semidirect |
| 24. C53×#349 | C4 | semidirect |
| 157. #349 | #6157 | semidirect |
| 161. C53 | #12613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811682 | 2 |
| #20290927 | 2 |
| #20290471 | 2 |
| #20289767 | 2 |
| #20276334 | 2 |
| #12613 | 53 |