Finite Group DatabasebetaFinite Group Databasebeta← C7×ΓL(1,𝔽8)×#63122 #50303843
Order 38220.
120 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 36 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. C72×#63122 | C3 | semidirect |
| 3. C5×C7×C13×ΓL(1,𝔽8) | C4 | semidirect |
| 7. ΓL(1,𝔽8)×#63122 | C7 | direct (N × H) |
| 9. C5×C72×C13 | C3×C4 | semidirect |
| 14. C7×C13×ΓL(1,𝔽8) | AGL(1,𝔽5) | semidirect |
| 16. C7×#63122 | ΓL(1,𝔽8) | direct (N × H) |
| 17. C7×#63122 | C3×C7 | semidirect |
| 20. C5×C13×ΓL(1,𝔽8) | C4×C7 | semidirect |
| 29. C5×C7×ΓL(1,𝔽8) | #261 | semidirect |
| 30. C72×C13 | C3×AGL(1,𝔽5) | semidirect |
| 36. C5×C7×C13 | C4×ΓL(1,𝔽8) | semidirect |
| 37. C5×C7×C13 | C3×C4×C7 | semidirect |
| 46. C13×ΓL(1,𝔽8) | C7×AGL(1,𝔽5) | semidirect |
| 47. #63122 | C7×ΓL(1,𝔽8) | direct (N × H) |
| 48. C5×C72 | C3×#261 | semidirect |
| 57. C7×ΓL(1,𝔽8) | #63122 | direct (N × H) |
| 63. C5×ΓL(1,𝔽8) | C7×#261 | semidirect |
| 66. C7×C13 | AGL(1,𝔽5)×ΓL(1,𝔽8) | semidirect |
| 67. C7×C13 | C3×C7×AGL(1,𝔽5) | semidirect |
| 74. C5×C13 | C4×C7×ΓL(1,𝔽8) | semidirect |
| 77. C72 | C3×#63122 | semidirect |
| 82. C5×C7 | ΓL(1,𝔽8)×#261 | semidirect |
| 83. C5×C7 | C3×C7×#261 | semidirect |
| 90. ΓL(1,𝔽8) | C7×#63122 | direct (N × H) |
| 96. C13 | C7×AGL(1,𝔽5)×ΓL(1,𝔽8) | semidirect |
| 100. C7 | ΓL(1,𝔽8)×#63122 | direct (N × H) |
| 101. C7 | C3×C7×#63122 | semidirect |
| 103. C5 | C7×ΓL(1,𝔽8)×#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×ΓL(1,𝔽8)×D65 | 2 |
| C72×#63122 | 3 |
| C7×ΓL(1,𝔽8)×#261 | 5 |
| C3×C7×#63122 | 7 |
| ΓL(1,𝔽8)×#63122 | 7 |
| C7×AGL(1,𝔽5)×ΓL(1,𝔽8) | 13 |