Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 1. C2×#16810457 | C2 | semidirect |
| 2. #20276499 | C2 | semidirect |
| 3. #20272902 | C2 | semidirect |
| 7. #16810457 | C22 | semidirect |
| 9. #16810451 | C22 | semidirect |
| 14. C53×#508 | C4 | semidirect |
| 16. C2×Q32×C53 | C4 | semidirect |
| 18. C2×D16×C53 | C4 | semidirect |
| 120. #508 | Dic53 | semidirect |
| 122. C2×Q32 | Dic53 | semidirect |
| 124. C2×D16 | Dic53 | semidirect |
| 132. C53 | #13622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810457 | 2 |
| #20276499 | 2 |
| #20272902 | 2 |
| C2×C53×#508 | 2 |
| #13622 | 53 |