Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
19742 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.
This group has 19742 conjugacy classes of subgroups — too many to draw. Only its 8408 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. C23×C4⋊#6157 | C2 | direct (N × H) |
| 6. C22×C4⋊#6157 | C22 | direct (N × H) |
| 8. C24×Dic53 | C4 | semidirect |
| 9. C23×C4×D53 | C4 | semidirect |
| 11. C24×C4×C53 | C4 | semidirect |
| 14. C2×C4⋊#6157 | C23 | direct (N × H) |
| 19. C23×Dic53 | C2×C4 | semidirect |
| 20. C22×C4×D53 | C2×C4 | semidirect |
| 23. C23×C4×C53 | C2×C4 | semidirect |
| 24. C24×C53 | C4⋊C4 | semidirect |
| 26. C23×D53 | C4⋊C4 | semidirect |
| 33. C22×C4×C53 | C22×C4 | semidirect |
| 34. C22×Dic53 | C22×C4 | semidirect |
| 35. C2×C4×D53 | C22×C4 | semidirect |
| 37. C4⋊#6157 | C24 | direct (N × H) |
| 38. C23×C53 | C2×C4⋊C4 | semidirect |
| 40. C22×D53 | C2×C4⋊C4 | semidirect |
| 47. C2×C4×C53 | C23×C4 | semidirect |
| 48. C2×Dic53 | C23×C4 | semidirect |
| 49. C4×D53 | C23×C4 | semidirect |
| 52. C22×C53 | C22×C4⋊C4 | semidirect |
| 54. C2×D53 | C22×C4⋊C4 | semidirect |
| 60. C4×C53 | C24×C4 | semidirect |
| 61. Dic53 | C24×C4 | semidirect |
| 65. C2×C53 | C23×C4⋊C4 | semidirect |
| 67. D53 | C23×C4⋊C4 | semidirect |
| 76. C24×C4 | #6157 | semidirect |
| 78. C53 | C24×C4⋊C4 | semidirect |
| 89. C23×C4 | C2×#6157 | semidirect |
| 96. C24 | C4⋊#6157 | direct (N × H) |
| 103. C22×C4 | C22×#6157 | semidirect |
| 110. C23 | C2×C4⋊#6157 | direct (N × H) |
| 117. C2×C4 | C23×#6157 | semidirect |
| 123. C22 | C22×C4⋊#6157 | direct (N × H) |
| 127. C4 | C24×#6157 | semidirect |
| 131. C2 | C23×C4⋊#6157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#6157 | 2 |
| C23×C4⋊#6157 | 2 |
| C24×C4×D53 | 2 |
| C24×C4⋊C4 | 53 |