Finite Group DatabasebetaFinite Group Databasebeta← C7×C25×C3⋊AGL(1,𝔽7) #36347742
Order 22050.
114 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 48 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×C7×ΓL(1,𝔽8)×C25 | C2 | semidirect |
| 2. C7×C25×D21 | C3 | semidirect |
| 6. C7×ΓL(1,𝔽8)×C25 | D3 | semidirect |
| 7. C3×C72×C25 | C2×C3 | semidirect |
| 9. C25×C3⋊AGL(1,𝔽7) | C7 | direct (N × H) |
| 13. C3×ΓL(1,𝔽8)×C25 | C2×C7 | semidirect |
| 16. C72×C25 | C3×D3 | semidirect |
| 18. C25×D21 | C3×C7 | semidirect |
| 21. C7×C3⋊AGL(1,𝔽7) | C25 | direct (N × H) |
| 30. C3×C7×C25 | AGL(1,𝔽7) | semidirect |
| 31. C3×C7×C25 | C2×C3×C7 | semidirect |
| 33. ΓL(1,𝔽8)×C25 | D3×C7 | semidirect |
| 36. C3×C7×ΓL(1,𝔽8) | C2×C25 | semidirect |
| 41. C7×D21 | C3×C25 | semidirect |
| 50. C7×C25 | C3⋊AGL(1,𝔽7) | direct (N × H) |
| 51. C7×C25 | C3×D3×C7 | semidirect |
| 54. C3×C72 | C2×C3×C25 | semidirect |
| 56. C7×ΓL(1,𝔽8) | D3×C25 | semidirect |
| 58. C3⋊AGL(1,𝔽7) | C7×C25 | direct (N × H) |
| 70. C3×C25 | C7×AGL(1,𝔽7) | semidirect |
| 74. C3×ΓL(1,𝔽8) | C2×C7×C25 | semidirect |
| 76. C72 | C3×D3×C25 | semidirect |
| 79. D21 | C3×C7×C25 | semidirect |
| 87. C25 | C7×C3⋊AGL(1,𝔽7) | direct (N × H) |
| 91. C3×C7 | C25×AGL(1,𝔽7) | semidirect |
| 92. C3×C7 | C2×C3×C7×C25 | semidirect |
| 94. ΓL(1,𝔽8) | D3×C7×C25 | semidirect |
| 104. C7 | C25×C3⋊AGL(1,𝔽7) | direct (N × H) |
| 105. C7 | C3×D3×C7×C25 | semidirect |
| 111. C3 | C7×C25×AGL(1,𝔽7) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×ΓL(1,𝔽8)×C25 | 2 |
| C7×C25×D21 | 3 |
| C7×C25×AGL(1,𝔽7) | 3 |
| C5×C7×C3⋊AGL(1,𝔽7) | 5 |
| C3×D3×C7×C25 | 7 |
| C25×C3⋊AGL(1,𝔽7) | 7 |