Finite Group DatabasebetaFinite Group Databasebeta← ΓL(1,𝔽8)×#13095531 #45657406
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. ΓL(1,𝔽8)×#11715913 | C2 | semidirect |
| 2. D37⋊#3862 | C3 | semidirect |
| 3. #24925974 | C3 | semidirect |
| 4. C7×ΓL(1,𝔽8)×D37 | C3 | semidirect |
| 5. C7×#13095531 | C3 | semidirect |
| 6. C37⋊#3862 | C2×C3 | semidirect |
| 7. #19129588 | C2×C3 | semidirect |
| 8. C7×#11715913 | C2×C3 | semidirect |
| 9. C7×ΓL(1,𝔽8)×C37 | C2×C3 | semidirect |
| 12. C72×D37 | C32 | semidirect |
| 15. C72×C37 | C2×C32 | semidirect |
| 22. #13095531 | ΓL(1,𝔽8) | direct (N × H) |
| 23. ΓL(1,𝔽8)×D37 | ΓL(1,𝔽8) | semidirect |
| 31. #11715913 | C2×ΓL(1,𝔽8) | semidirect |
| 34. ΓL(1,𝔽8)×C37 | C2×ΓL(1,𝔽8) | semidirect |
| 37. C7×D37 | C3×ΓL(1,𝔽8) | semidirect |
| 38. C7×D37 | C3×ΓL(1,𝔽8) | semidirect |
| 46. C7×C37 | C2×C3×ΓL(1,𝔽8) | semidirect |
| 47. C7×C37 | C2×C3×ΓL(1,𝔽8) | semidirect |
| 55. C7×ΓL(1,𝔽8) | D37⋊C3 | semidirect |
| 63. D37 | ΓL(1,𝔽8)2 | semidirect |
| 66. C72 | C3×D37⋊C3 | semidirect |
| 76. C37 | C2×ΓL(1,𝔽8)2 | semidirect |
| 85. ΓL(1,𝔽8) | #13095531 | direct (N × H) |
| 92. C7 | ΓL(1,𝔽8)×D37⋊C3 | semidirect |
| 93. C7 | C3×#13095531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#11715913 | 2 |
| D37⋊#3862 | 3 |
| #24925974 | 3 |
| C7×ΓL(1,𝔽8)×D37 | 3 |
| C7×#13095531 | 3 |
| C3×#13095531 | 7 |
| ΓL(1,𝔽8)×D37⋊C3 | 7 |
| C2×ΓL(1,𝔽8)2 | 37 |