Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
43678 conjugacy classes of subgroups; only the 13003 normal subgroups are shown.
This group has 43678 conjugacy classes of subgroups — too many to draw. Only its 13003 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. C25×Dic17 | C2 | semidirect |
| 2. C23×C22⋊Dic17 | C2 | direct (N × H) |
| 5. C24×Dic17 | C22 | semidirect |
| 6. C22×C22⋊Dic17 | C22 | direct (N × H) |
| 8. C26×C17 | C4 | semidirect |
| 14. C25×C17 | C2×C4 | semidirect |
| 19. C23×Dic17 | C23 | semidirect |
| 20. C2×C22⋊Dic17 | C23 | direct (N × H) |
| 23. C24×C17 | C22⋊C4 | semidirect |
| 25. C24×C17 | C22×C4 | semidirect |
| 30. C22×Dic17 | C24 | semidirect |
| 31. C22⋊Dic17 | C24 | direct (N × H) |
| 35. C23×C17 | C2×C22⋊C4 | semidirect |
| 37. C23×C17 | C23×C4 | semidirect |
| 42. C2×Dic17 | C25 | semidirect |
| 48. C22×C17 | C22×C22⋊C4 | semidirect |
| 50. C22×C17 | C24×C4 | semidirect |
| 55. C26 | Dic17 | semidirect |
| 62. C2×C17 | C23×C22⋊C4 | semidirect |
| 68. C25 | C2×Dic17 | semidirect |
| 75. C17 | C24×C22⋊C4 | semidirect |
| 78. C24 | C22⋊Dic17 | direct (N × H) |
| 80. C24 | C22×Dic17 | semidirect |
| 89. C23 | C2×C22⋊Dic17 | direct (N × H) |
| 91. C23 | C23×Dic17 | semidirect |
| 99. C22 | C22×C22⋊Dic17 | direct (N × H) |
| 101. C22 | C24×Dic17 | semidirect |
| 106. C2 | C23×C22⋊Dic17 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×Dic17 | 2 |
| C23×C22⋊Dic17 | 2 |
| C27×C17 | 2 |
| C24×C22⋊C4 | 17 |