Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2830 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2830 conjugacy classes of subgroups — too many to draw. Only its 747 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. C22×#13133209 | C2 | semidirect |
| 2. C2×#16810987 | C2 | direct (N × H) |
| 3. C22×#13133138 | C2 | semidirect |
| 4. C22×#13133128 | C2 | semidirect |
| 8. C2×#13133209 | C22 | semidirect |
| 11. #16810987 | C22 | direct (N × H) |
| 12. C2×#13133138 | C22 | semidirect |
| 13. C2×#13133128 | C22 | semidirect |
| 23. #13133209 | C23 | semidirect |
| 27. #13133138 | C23 | semidirect |
| 28. #13133128 | C23 | semidirect |
| 88. C22×C53 | #490 | semidirect |
| 102. C2×C53 | C2×#490 | semidirect |
| 118. C53 | C22×#490 | semidirect |
| 187. C22 | #16810987 | direct (N × H) |
| 196. C2 | C2×#16810987 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133209 | 2 |
| C2×#16810987 | 2 |
| C22×#13133138 | 2 |
| C22×#13133128 | 2 |
| C22×#127×C53 | 2 |
| C22×#490 | 53 |