Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
14334 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 14334 conjugacy classes of subgroups — too many to draw. Only its 4427 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. C24×Dic106 | C2 | semidirect |
| 3. C22×#13133205 | C2 | direct (N × H) |
| 4. C23×#11719921 | C2 | semidirect |
| 5. C23×C42×C53 | C2 | semidirect |
| 8. C23×Dic106 | C22 | semidirect |
| 12. C2×#13133205 | C22 | direct (N × H) |
| 13. C22×#11719921 | C22 | semidirect |
| 16. C22×C42×C53 | C22 | semidirect |
| 21. C22×Dic106 | C23 | semidirect |
| 26. #13133205 | C23 | direct (N × H) |
| 27. C2×#11719921 | C23 | semidirect |
| 33. C2×C42×C53 | C23 | semidirect |
| 50. C2×Dic106 | C24 | semidirect |
| 51. C42×C53 | C24 | semidirect |
| 52. #11719921 | C24 | semidirect |
| 53. C23×C53 | #124 | semidirect |
| 70. C22×C53 | C2×#124 | semidirect |
| 84. C23×C42 | D53 | semidirect |
| 85. C2×C53 | C22×#124 | semidirect |
| 99. C22×C42 | C2×D53 | semidirect |
| 100. C53 | C23×#124 | semidirect |
| 117. C2×C42 | C22×D53 | semidirect |
| 136. C42 | C23×D53 | semidirect |
| 141. C23 | #13133205 | direct (N × H) |
| 156. C22 | C2×#13133205 | direct (N × H) |
| 164. C2 | C22×#13133205 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic106 | 2 |
| C24×D212 | 2 |
| C22×#13133205 | 2 |
| C23×#11719921 | 2 |
| C23×C42×C53 | 2 |
| C23×#124 | 53 |