Finite Group DatabasebetaFinite Group DatabasebetaOrder 3528.
480 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 102 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×C4×#3861 | C2 | semidirect |
| 3. C3×#10596874 | C2 | semidirect |
| 4. C3×C4×C7⋊D7 | C3 | semidirect |
| 5. C4×#64424 | C3 | direct (N × H) |
| 7. C3×#64424 | C4 | direct (N × H) |
| 8. C3×#64424 | C4 | direct (N × H) |
| 11. C3×C4×C72 | C2×C3 | semidirect |
| 12. C3×C7⋊Dic7 | C2×C3 | semidirect |
| 13. C4×#3861 | C2×C3 | semidirect |
| 14. #10596874 | C2×C3 | semidirect |
| 19. C3×#3861 | C2×C4 | semidirect |
| 20. C4×C7⋊D7 | C32 | semidirect |
| 22. C3×C7⋊D7 | C3×C4 | semidirect |
| 23. C3×C7⋊D7 | C3×C4 | semidirect |
| 25. #64424 | C3×C4 | direct (N × H) |
| 26. #64424 | C3×C4 | direct (N × H) |
| 40. C4×C72 | C2×C32 | semidirect |
| 41. C7⋊Dic7 | C2×C32 | semidirect |
| 50. C3×C72 | C2×C3×C4 | semidirect |
| 51. #3861 | C2×C3×C4 | semidirect |
| 65. C7⋊D7 | C32×C4 | semidirect |
| 66. C7⋊D7 | C32×C4 | semidirect |
| 75. C3×C4×C7 | AGL(1,𝔽7) | semidirect |
| 76. C3×C4×C7 | AGL(1,𝔽7) | semidirect |
| 77. C3×C4×C7 | AGL(1,𝔽7) | semidirect |
| 78. C3×C4×C7 | AGL(1,𝔽7) | semidirect |
| 100. C72 | C2×C32×C4 | semidirect |
| 132. C4×C7 | C3×AGL(1,𝔽7) | semidirect |
| 133. C4×C7 | C3×AGL(1,𝔽7) | semidirect |
| 134. C4×C7 | C3×AGL(1,𝔽7) | semidirect |
| 135. C4×C7 | C3×AGL(1,𝔽7) | semidirect |
| 142. C3×C7 | C4×AGL(1,𝔽7) | semidirect |
| 143. C3×C7 | C4×AGL(1,𝔽7) | semidirect |
| 144. C3×C7 | C4×AGL(1,𝔽7) | semidirect |
| 145. C3×C7 | C4×AGL(1,𝔽7) | semidirect |
| 170. C3×C4 | #64424 | direct (N × H) |
| 173. C7 | C3×C4×AGL(1,𝔽7) | semidirect |
| 174. C7 | C3×C4×AGL(1,𝔽7) | semidirect |
| 175. C7 | C3×C4×AGL(1,𝔽7) | semidirect |
| 176. C7 | C3×C4×AGL(1,𝔽7) | semidirect |
| 185. C4 | C3×#64424 | direct (N × H) |
| 187. C3 | C4×#64424 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#64424 | 2 |
| C3×C4×#3861 | 2 |
| C3×#10596874 | 2 |
| C3×C4×C7⋊D7 | 3 |
| C4×#64424 | 3 |
| C3×C4×AGL(1,𝔽7) | 7 |