Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
456 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 146 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 |
|---|---|---|
| 1. C3×D4×AGL(1,𝔽7) | C2 | semidirect |
| 2. C3×D8×ΓL(1,𝔽8) | C2 | semidirect |
| 3. C3×#1141⋊C3 | C2 | semidirect |
| 4. C3×D56⋊C3 | C2 | semidirect |
| 5. C3×C8×AGL(1,𝔽7) | C2 | semidirect |
| 6. C3×D7×D8 | C3 | semidirect |
| 7. D8×AGL(1,𝔽7) | C3 | direct (N × H) |
| 9. C3×D4×ΓL(1,𝔽8) | C22 | semidirect |
| 11. C3×C4⋊AGL(1,𝔽7) | C22 | semidirect |
| 13. C3×C8×ΓL(1,𝔽8) | C22 | semidirect |
| 14. C3×ΓL(1,𝔽8)⋊C8 | C22 | semidirect |
| 15. C3×D4×D7 | C2×C3 | semidirect |
| 16. D4×AGL(1,𝔽7) | C2×C3 | semidirect |
| 17. C3×C7×D8 | C2×C3 | semidirect |
| 18. C3×#1141 | C2×C3 | semidirect |
| 19. C3×D56 | C2×C3 | semidirect |
| 20. C3×C8×D7 | C2×C3 | semidirect |
| 21. D8×ΓL(1,𝔽8) | C2×C3 | semidirect |
| 22. #1141⋊C3 | C2×C3 | semidirect |
| 23. D56⋊C3 | C2×C3 | semidirect |
| 24. C8×AGL(1,𝔽7) | C2×C3 | semidirect |
| 32. D7×D8 | C32 | semidirect |
| 35. C3×C7×D4 | C22×C3 | semidirect |
| 37. C3×D28 | C22×C3 | semidirect |
| 39. D4×ΓL(1,𝔽8) | C22×C3 | semidirect |
| 41. C4⋊AGL(1,𝔽7) | C22×C3 | semidirect |
| 43. C3×C7×C8 | C22×C3 | semidirect |
| 44. C3×C7⋊C8 | C22×C3 | semidirect |
| 45. C8×ΓL(1,𝔽8) | C22×C3 | semidirect |
| 46. ΓL(1,𝔽8)⋊C8 | C22×C3 | semidirect |
| 55. C3×AGL(1,𝔽7) | D8 | direct (N × H) |
| 56. D4×D7 | C2×C32 | semidirect |
| 57. C7×D8 | C2×C32 | semidirect |
| 58. #1141 | C2×C32 | semidirect |
| 59. D56 | C2×C32 | semidirect |
| 60. C8×D7 | C2×C32 | semidirect |
| 82. C3×ΓL(1,𝔽8) | C2×D8 | semidirect |
| 84. C7×D4 | C22×C32 | semidirect |
| 86. D28 | C22×C32 | semidirect |
| 88. C7×C8 | C22×C32 | semidirect |
| 89. C7⋊C8 | C22×C32 | semidirect |
| 97. C3×D8 | AGL(1,𝔽7) | direct (N × H) |
| 103. C3×D7 | C3×D8 | semidirect |
| 107. AGL(1,𝔽7) | C3×D8 | direct (N × H) |
| 128. C3×D4 | C2×AGL(1,𝔽7) | semidirect |
| 134. C3×C8 | C2×AGL(1,𝔽7) | semidirect |
| 135. C3×C7 | C2×C3×D8 | semidirect |
| 136. ΓL(1,𝔽8) | C2×C3×D8 | semidirect |
| 144. D8 | C3×AGL(1,𝔽7) | direct (N × H) |
| 149. D7 | C32×D8 | semidirect |
| 166. D4 | C2×C3×AGL(1,𝔽7) | semidirect |
| 169. C8 | C2×C3×AGL(1,𝔽7) | semidirect |
| 170. C7 | C2×C32×D8 | semidirect |
| 186. C3 | D8×AGL(1,𝔽7) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×AGL(1,𝔽7) | 2 |
| C3×D8×ΓL(1,𝔽8) | 2 |
| C3×#1141⋊C3 | 2 |
| C3×D56⋊C3 | 2 |
| C3×C8×AGL(1,𝔽7) | 2 |
| C3×D7×D8 | 3 |
| D8×AGL(1,𝔽7) | 3 |
| C2×C32×D8 | 7 |