Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20276326 | C2 | semidirect |
| 3. #20272723 | C2 | semidirect |
| 4. C53×#1807 | C2 | semidirect |
| 5. C22×D424 | C4 | semidirect |
| 10. #16810859 | C4 | semidirect |
| 12. C2×#13133151 | C4 | semidirect |
| 15. C22⋊#11719908 | C22 | semidirect |
| 19. C53×#340 | C22 | semidirect |
| 150. #1807 | D53 | semidirect |
| 173. #340 | C2×D53 | semidirect |
| 174. C53 | #11888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810859 | 2 |
| #20276326 | 2 |
| #20272723 | 2 |
| C53×#1807 | 2 |
| #11888 | 53 |