Finite Group DatabasebetaFinite Group Databasebeta← D7×ΓL(1,𝔽8)×C19⋊C3 #30660721
Order 16758.
100 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 33 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×C19 | C2×C32 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×ΓL(1,𝔽8)×C19⋊C3 | C2 | semidirect |
| 2. D7×#87705 | C3 | semidirect |
| 3. D7×#87704 | C3 | semidirect |
| 4. D7×C19×ΓL(1,𝔽8) | C3 | semidirect |
| 5. C7×D7×C19⋊C3 | C3 | semidirect |
| 6. C7×#87705 | C2×C3 | semidirect |
| 7. C7×#87704 | C2×C3 | semidirect |
| 8. C7×C19×ΓL(1,𝔽8) | C2×C3 | semidirect |
| 9. C72×C19⋊C3 | C2×C3 | semidirect |
| 12. C7×D7×C19 | C32 | semidirect |
| 14. ΓL(1,𝔽8)×C19⋊C3 | D7 | direct (N × H) |
| 15. C72×C19 | C2×C32 | semidirect |
| 24. D7×C19⋊C3 | ΓL(1,𝔽8) | direct (N × H) |
| 27. #87705 | C3×D7 | semidirect |
| 28. #87704 | C3×D7 | semidirect |
| 32. C7×C19⋊C3 | C2×ΓL(1,𝔽8) | semidirect |
| 33. C7×C19⋊C3 | C3×D7 | semidirect |
| 34. C19×ΓL(1,𝔽8) | C3×D7 | semidirect |
| 39. D7×ΓL(1,𝔽8) | C19⋊C3 | direct (N × H) |
| 41. D7×C19 | C3×ΓL(1,𝔽8) | semidirect |
| 46. C7×ΓL(1,𝔽8) | C2×C19⋊C3 | semidirect |
| 48. C7×C19 | C2×C3×ΓL(1,𝔽8) | semidirect |
| 49. C7×C19 | C32×D7 | semidirect |
| 56. C7×D7 | C3×C19⋊C3 | semidirect |
| 62. C19⋊C3 | D7×ΓL(1,𝔽8) | direct (N × H) |
| 63. C72 | C2×C3×C19⋊C3 | semidirect |
| 81. ΓL(1,𝔽8) | D7×C19⋊C3 | direct (N × H) |
| 82. C19 | C3×D7×ΓL(1,𝔽8) | semidirect |
| 85. D7 | ΓL(1,𝔽8)×C19⋊C3 | direct (N × H) |
| 88. C7 | C2×ΓL(1,𝔽8)×C19⋊C3 | semidirect |
| 89. C7 | C3×D7×C19⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×ΓL(1,𝔽8)×C19⋊C3 | 2 |
| D7×#87705 | 3 |
| D7×#87704 | 3 |
| D7×C19×ΓL(1,𝔽8) | 3 |
| C7×D7×C19⋊C3 | 3 |
| C3×D7×C19⋊C3 | 7 |
| C2×ΓL(1,𝔽8)×C19⋊C3 | 7 |
| C3×D7×ΓL(1,𝔽8) | 19 |