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 |
|---|---|---|
| 2. C22×#13133209 | C2 | semidirect |
| 3. C2×#16810988 | C2 | direct (N × H) |
| 4. C22×#13133139 | C2 | semidirect |
| 5. C22×#97×C53 | C2 | semidirect |
| 11. C2×#13133209 | C22 | semidirect |
| 14. #16810988 | C22 | direct (N × H) |
| 15. C2×#13133139 | C22 | semidirect |
| 18. C2×#97×C53 | C22 | semidirect |
| 29. #13133209 | C23 | semidirect |
| 33. #13133139 | C23 | semidirect |
| 40. #97×C53 | C23 | semidirect |
| 85. C22×C53 | #490 | semidirect |
| 100. C22×#97 | D53 | semidirect |
| 101. C2×C53 | C2×#490 | semidirect |
| 117. C2×#97 | C2×D53 | semidirect |
| 118. C53 | C22×#490 | semidirect |
| 140. #97 | C22×D53 | semidirect |
| 187. C22 | #16810988 | direct (N × H) |
| 196. C2 | C2×#16810988 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133214 | 2 |
| C22×#13133209 | 2 |
| C2×#16810988 | 2 |
| C22×#13133139 | 2 |
| C22×#97×C53 | 2 |
| C22×#490 | 53 |