Finite Group DatabasebetaFinite Group DatabasebetaOrder 3528.
282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #64423 |
| commutator, hypocenter | C72 | C2×C32×C4 |
| Frattini | C2 | C2×C3×#64423 |
| Fitting, socle | C22×C3×C72 | C2×C3 |
| prime radical | C22×C3×#3861 | C2 |
| cosocle | C2×C72 | C22×C32 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C22×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#10596873 | C2 | direct (N × H) |
| 3. C2×C3×C7×Dic7 | C3 | semidirect |
| 4. C2×#10596873 | C3 | direct (N × H) |
| 5. C2×C3×#3861 | C4 | semidirect |
| 9. C3×C7×Dic7 | C2×C3 | semidirect |
| 10. #10596873 | C2×C3 | direct (N × H) |
| 13. C3×#3861 | C2×C4 | semidirect |
| 14. C2×C7×Dic7 | C32 | semidirect |
| 15. C2×C3×C72 | C3×C4 | semidirect |
| 17. C2×#3861 | C3×C4 | semidirect |
| 25. C7×Dic7 | C2×C32 | semidirect |
| 27. C2×C3×Dic7 | ΓL(1,𝔽8) | semidirect |
| 30. C3×C72 | C2×C3×C4 | semidirect |
| 31. #3861 | C2×C3×C4 | semidirect |
| 38. C2×C72 | C32×C4 | semidirect |
| 47. C3×Dic7 | C2×ΓL(1,𝔽8) | semidirect |
| 55. C2×Dic7 | C3×ΓL(1,𝔽8) | semidirect |
| 56. C72 | C2×C32×C4 | semidirect |
| 59. C2×C3×C7 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 60. C2×C3×C7 | C4×ΓL(1,𝔽8) | semidirect |
| 75. Dic7 | C2×C3×ΓL(1,𝔽8) | semidirect |
| 79. C3×C7 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 80. C3×C7 | C2×C4×ΓL(1,𝔽8) | semidirect |
| 88. C2×C7 | C3×ΓL(1,𝔽8)⋊C4 | semidirect |
| 89. C2×C7 | C3×C4×ΓL(1,𝔽8) | semidirect |
| 99. C7 | C2×C3×ΓL(1,𝔽8)⋊C4 | semidirect |
| 100. C7 | C2×C3×C4×ΓL(1,𝔽8) | semidirect |
| 103. C2×C3 | #10596873 | direct (N × H) |
| 108. C3 | C2×#10596873 | direct (N × H) |
| 109. 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×C3×C7×Dic7 | 3 |
| C2×#10596873 | 3 |
| C2×C3×C4×ΓL(1,𝔽8) | 7 |
| C2×C3×ΓL(1,𝔽8)⋊C4 | 7 |