Finite Group DatabasebetaFinite Group Databasebeta← ΓL(1,𝔽8)⋊#13095536 #45657437
Order 32634.
112 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 25 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. ΓL(1,𝔽8)×#11715912 | C2 | semidirect |
| 2. #24925972 | C3 | semidirect |
| 3. C37×ΓL(1,𝔽8)⋊D7 | C3 | semidirect |
| 4. #24925954 | C3 | semidirect |
| 5. #24925950 | C3 | semidirect |
| 6. C37⋊#3862 | C2×C3 | semidirect |
| 7. #19129589 | C2×C3 | semidirect |
| 8. C7×#11715912 | C2×C3 | semidirect |
| 9. C7×ΓL(1,𝔽8)×C37 | C2×C3 | semidirect |
| 12. C37×C7⋊D7 | C32 | semidirect |
| 15. C72×C37 | C2×C32 | semidirect |
| 32. #11715912 | AGL(1,𝔽7) | semidirect |
| 34. ΓL(1,𝔽8)×C37 | AGL(1,𝔽7) | semidirect |
| 44. ΓL(1,𝔽8)⋊D7 | C37⋊C3 | semidirect |
| 46. C7×C37 | C3×AGL(1,𝔽7) | semidirect |
| 47. C7×C37 | C3×AGL(1,𝔽7) | semidirect |
| 55. C7×ΓL(1,𝔽8) | C2×C37⋊C3 | semidirect |
| 62. C7⋊D7 | C3×C37⋊C3 | semidirect |
| 66. C72 | C2×C3×C37⋊C3 | semidirect |
| 76. C37 | ΓL(1,𝔽8)⋊AGL(1,𝔽7) | semidirect |
| 85. ΓL(1,𝔽8) | #13095536 | semidirect |
| 92. C7 | AGL(1,𝔽7)×C37⋊C3 | semidirect |
| 93. C7 | C3×#13095536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#11715912 | 2 |
| #24925972 | 3 |
| C37×ΓL(1,𝔽8)⋊D7 | 3 |
| #24925954 | 3 |
| #24925950 | 3 |
| C3×#13095536 | 7 |
| AGL(1,𝔽7)×C37⋊C3 | 7 |
| ΓL(1,𝔽8)⋊AGL(1,𝔽7) | 37 |