Finite Group DatabasebetaFinite Group DatabasebetaOrder 29988.
184 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 46 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. C7×C17×Dic21 | C3 | semidirect |
| 4. C3×C17×#3861 | C4 | semidirect |
| 12. C17×#3861 | Dic3 | semidirect |
| 13. C3×C72×C17 | C3×C4 | semidirect |
| 17. C3⋊#10596873 | C17 | direct (N × H) |
| 19. C17×Dic21 | ΓL(1,𝔽8) | semidirect |
| 27. C72×C17 | C3×Dic3 | semidirect |
| 38. C7×Dic21 | C3×C17 | semidirect |
| 42. C3×#3861 | C4×C17 | semidirect |
| 44. C3×C7×C17 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 45. C3×C7×C17 | C4×ΓL(1,𝔽8) | semidirect |
| 65. C3×C72 | C3×C4×C17 | semidirect |
| 67. #3861 | Dic3×C17 | semidirect |
| 72. C7×C17 | Dic3×ΓL(1,𝔽8) | semidirect |
| 73. C7×C17 | C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 78. Dic21 | C17×ΓL(1,𝔽8) | semidirect |
| 88. C3×C17 | #10596873 | semidirect |
| 89. C72 | C3×Dic3×C17 | semidirect |
| 104. C3×C7 | C17×ΓL(1,𝔽8)⋊C4 | semidirect |
| 105. C3×C7 | C4×C17×ΓL(1,𝔽8) | semidirect |
| 113. C17 | C3⋊#10596873 | direct (N × H) |
| 121. C7 | C17×C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 122. C7 | Dic3×C17×ΓL(1,𝔽8) | semidirect |
| 129. C3 | C17×#10596873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C17×#3861 | 2 |
| C7×C17×Dic21 | 3 |
| C17×#10596873 | 3 |
| Dic3×C17×ΓL(1,𝔽8) | 7 |
| C17×C3⋊(ΓL(1,𝔽8)⋊C4) | 7 |
| C3⋊#10596873 | 17 |