Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
324 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×#16810460 | C2 | semidirect |
| 3. #20276803 | C2 | semidirect |
| 4. #20272894 | C2 | semidirect |
| 5. #20272893 | C2 | semidirect |
| 6. #20272852 | C2 | semidirect |
| 7. C2×C53×SD64 | C2 | semidirect |
| 16. C2×#13133123 | C22 | semidirect |
| 17. #16810449 | C22 | semidirect |
| 19. C2×Q32×C53 | C22 | semidirect |
| 22. C2×C32×C53 | C22 | semidirect |
| 105. C2×D53 | SD64 | semidirect |
| 113. C2×SD64 | D53 | semidirect |
| 125. C2×Q32 | C2×D53 | semidirect |
| 136. C2×C32 | C2×D53 | semidirect |
| 139. C53 | #13664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D53 | 2 |
| C2×#16810460 | 2 |
| #20276803 | 2 |
| #20272894 | 2 |
| #20272893 | 2 |
| #20272852 | 2 |
| C2×C53×SD64 | 2 |
| #13664 | 53 |