Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 107 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×#16810457 | C2 | semidirect |
| 3. #20272901 | C2 | direct (N × H) |
| 4. C2×C53×#367 | C2 | semidirect |
| 8. #16811055 | C4 | semidirect |
| 10. C2×Dic424 | C4 | semidirect |
| 12. C2×D848 | C4 | semidirect |
| 14. #16810457 | C22 | semidirect |
| 19. C53×#367 | C22 | semidirect |
| 29. Dic424 | C2×C4 | semidirect |
| 33. D848 | C2×C4 | semidirect |
| 111. C2×#367 | D53 | semidirect |
| 115. C2×C53 | #1418 | semidirect |
| 132. #367 | C2×D53 | semidirect |
| 133. C53 | C2×#1418 | semidirect |
| 225. C2 | #20272901 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811055 | 2 |
| C2×#16810457 | 2 |
| #20272901 | 2 |
| C2×C53×#367 | 2 |
| C2×#1418 | 53 |