Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
19742 conjugacy classes of subgroups; only the 13003 normal subgroups are shown.
This group has 19742 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 |
|---|---|---|
| 2. C23×C4⋊Dic17 | C2 | direct (N × H) |
| 6. C22×C4⋊Dic17 | C22 | direct (N × H) |
| 8. C24×C4×C17 | C4 | semidirect |
| 14. C23×C4×C17 | C2×C4 | semidirect |
| 18. C2×C4⋊Dic17 | C23 | direct (N × H) |
| 19. C24×C17 | C4⋊C4 | semidirect |
| 24. C22×C4×C17 | C22×C4 | semidirect |
| 28. C4⋊Dic17 | C24 | direct (N × H) |
| 30. C23×C17 | C2×C4⋊C4 | semidirect |
| 35. C2×C4×C17 | C23×C4 | semidirect |
| 42. C22×C17 | C22×C4⋊C4 | semidirect |
| 47. C4×C17 | C24×C4 | semidirect |
| 52. C24×C4 | Dic17 | semidirect |
| 55. C2×C17 | C23×C4⋊C4 | semidirect |
| 65. C23×C4 | C2×Dic17 | semidirect |
| 68. C17 | C24×C4⋊C4 | semidirect |
| 69. C24 | C4⋊Dic17 | direct (N × H) |
| 76. C22×C4 | C22×Dic17 | semidirect |
| 79. C23 | C2×C4⋊Dic17 | direct (N × H) |
| 86. C2×C4 | C23×Dic17 | semidirect |
| 88. C22 | C22×C4⋊Dic17 | direct (N × H) |
| 94. C4 | C24×Dic17 | semidirect |
| 95. C2 | C23×C4⋊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×C4⋊Dic17 | 2 |
| C25×C4×C17 | 2 |
| C24×C4⋊C4 | 17 |