Finite Group DatabasebetaFinite Group DatabasebetaOrder 3528.
238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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. C3⋊#10596873 | C2 | direct (N × H) |
| 3. C2×C7×Dic21 | C3 | semidirect |
| 5. C2×C3×#3861 | C4 | semidirect |
| 10. C7×Dic21 | C2×C3 | semidirect |
| 14. C3×#3861 | C2×C4 | semidirect |
| 16. C2×C3×C72 | C3×C4 | semidirect |
| 20. C2×#3861 | Dic3 | semidirect |
| 29. C2×Dic21 | ΓL(1,𝔽8) | semidirect |
| 33. C3×C72 | C2×C3×C4 | semidirect |
| 35. #3861 | C2×Dic3 | semidirect |
| 42. C2×C72 | C3×Dic3 | semidirect |
| 53. Dic21 | C2×ΓL(1,𝔽8) | semidirect |
| 63. C72 | C2×C3×Dic3 | semidirect |
| 66. C2×C3×C7 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 67. C2×C3×C7 | C4×ΓL(1,𝔽8) | semidirect |
| 92. C3×C7 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 93. C3×C7 | C2×C4×ΓL(1,𝔽8) | semidirect |
| 104. C2×C7 | Dic3×ΓL(1,𝔽8) | semidirect |
| 105. C2×C7 | C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 116. C7 | C2×Dic3×ΓL(1,𝔽8) | semidirect |
| 117. C7 | C2×C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 122. C2×C3 | #10596873 | semidirect |
| 128. C3 | C2×#10596873 | semidirect |
| 129. C2 | C3⋊#10596873 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#3861 | 2 |
| C3⋊#10596873 | 2 |
| C2×C7×Dic21 | 3 |
| C2×#10596873 | 3 |
| C2×C3⋊(ΓL(1,𝔽8)⋊C4) | 7 |
| C2×Dic3×ΓL(1,𝔽8) | 7 |