Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3678 conjugacy classes of subgroups; only the 1219 normal subgroups are shown.
This group has 3678 conjugacy classes of subgroups — too many to draw. Only its 1219 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×#16810491 | C2 | semidirect |
| 3. C2×#16810490 | C2 | semidirect |
| 4. #383×D53 | C2 | direct (N × H) |
| 6. C2×C53×#383 | C2 | semidirect |
| 10. C2×C42×D53 | C4 | semidirect |
| 12. #16810491 | C22 | semidirect |
| 13. #16810490 | C22 | semidirect |
| 18. C53×#383 | C22 | semidirect |
| 28. C2×C4×Dic53 | C2×C4 | semidirect |
| 30. C42×D53 | C2×C4 | semidirect |
| 35. C2×C42×C53 | C2×C4 | semidirect |
| 57. C42×C53 | C22×C4 | semidirect |
| 58. C4×Dic53 | C22×C4 | semidirect |
| 83. C2×D53 | #383 | direct (N × H) |
| 94. C2×#383 | D53 | direct (N × H) |
| 96. C2×C53 | C2×#383 | semidirect |
| 99. D53 | C2×#383 | direct (N × H) |
| 108. #383 | C2×D53 | direct (N × H) |
| 113. C53 | C22×#383 | semidirect |
| 127. C2×C42 | C4×D53 | semidirect |
| 152. C42 | C2×C4×D53 | semidirect |
| 184. C2 | #383×D53 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C42×D53 | 2 |
| C2×#16810491 | 2 |
| C2×#16810490 | 2 |
| #383×D53 | 2 |
| C2×#95×D53 | 2 |
| C2×C53×#383 | 2 |
| C22×#383 | 53 |