Finite Group DatabasebetaFinite Group Databasebeta← ΓL(1,𝔽8)⋊((C37⋊C3)⋊D7) #45657404
Order 32634.
112 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C37 | C2×C32 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×ΓL(1,𝔽8)×C37⋊C3 | C2 | semidirect |
| 2. (C37⋊C3)⋊(C7⋊D7) | C3 | semidirect |
| 3. ΓL(1,𝔽8)⋊D259 | C3 | semidirect |
| 4. #24925970 | C3 | semidirect |
| 5. #24925969 | C3 | semidirect |
| 6. C7×#11715912 | C2×C3 | semidirect |
| 7. C7×#11715913 | C2×C3 | semidirect |
| 8. C7×ΓL(1,𝔽8)×C37 | C2×C3 | semidirect |
| 9. C72×C37⋊C3 | C2×C3 | semidirect |
| 12. C7⋊D259 | C32 | semidirect |
| 14. ΓL(1,𝔽8)×C37⋊C3 | D7 | semidirect |
| 15. C72×C37 | C2×C32 | semidirect |
| 27. #11715913 | C3×D7 | semidirect |
| 28. #11715912 | C3×D7 | semidirect |
| 32. C7×C37⋊C3 | AGL(1,𝔽7) | semidirect |
| 33. C7×C37⋊C3 | C3×D7 | semidirect |
| 34. ΓL(1,𝔽8)×C37 | C3×D7 | semidirect |
| 46. C7×C37 | C3×AGL(1,𝔽7) | semidirect |
| 47. C7×C37 | C32×D7 | semidirect |
| 55. C7×ΓL(1,𝔽8) | D37⋊C3 | semidirect |
| 61. C37⋊C3 | ΓL(1,𝔽8)⋊D7 | semidirect |
| 66. C72 | C3×D37⋊C3 | semidirect |
| 76. C37 | C3×ΓL(1,𝔽8)⋊D7 | semidirect |
| 85. ΓL(1,𝔽8) | (C37⋊C3)⋊D7 | semidirect |
| 92. C7 | ΓL(1,𝔽8)⋊(D37⋊C3) | semidirect |
| 93. C7 | C3×(C37⋊C3)⋊D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×ΓL(1,𝔽8)×C37⋊C3 | 2 |
| (C37⋊C3)⋊(C7⋊D7) | 3 |
| ΓL(1,𝔽8)⋊D259 | 3 |
| #24925970 | 3 |
| #24925969 | 3 |
| C3×(C37⋊C3)⋊D7 | 7 |
| ΓL(1,𝔽8)⋊(D37⋊C3) | 7 |
| C3×ΓL(1,𝔽8)⋊D7 | 37 |