Finite Group DatabasebetaFinite Group Databasebeta← ΓL(1,𝔽8)×C22⋊#87704 #45692498
Order 33516.
132 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 29 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 | C22×C72×C19 | C32 |
| LCS | G ▷ C22×C72×C19 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C7×C19×ΓL(1,𝔽8) | C3 | semidirect |
| 2. C22⋊#14584115 | C3 | semidirect |
| 3. C7×C22⋊#87704 | C3 | semidirect |
| 4. C22⋊(C19⋊#3862) | C3 | semidirect |
| 9. C22×C72×C19 | C32 | semidirect |
| 13. C7×C19×ΓL(1,𝔽8) | A4 | semidirect |
| 22. C22⋊#87704 | ΓL(1,𝔽8) | direct (N × H) |
| 24. C22×C19×ΓL(1,𝔽8) | ΓL(1,𝔽8) | semidirect |
| 27. C72×C19 | C3×A4 | semidirect |
| 34. C22×C7×ΓL(1,𝔽8) | C19⋊C3 | semidirect |
| 36. C22×C7×C19 | C3×ΓL(1,𝔽8) | semidirect |
| 37. C22×C7×C19 | C3×ΓL(1,𝔽8) | semidirect |
| 47. C19×ΓL(1,𝔽8) | C22⋊ΓL(1,𝔽8) | semidirect |
| 58. C22×C72 | C3×C19⋊C3 | semidirect |
| 63. C7×ΓL(1,𝔽8) | C22⋊(C19⋊C3) | semidirect |
| 65. C7×C19 | A4×ΓL(1,𝔽8) | semidirect |
| 66. C7×C19 | C3×C22⋊ΓL(1,𝔽8) | semidirect |
| 77. C22×ΓL(1,𝔽8) | #87704 | semidirect |
| 78. C22×C19 | ΓL(1,𝔽8)2 | semidirect |
| 85. C72 | C3×C22⋊(C19⋊C3) | semidirect |
| 91. C22×C7 | ΓL(1,𝔽8)×C19⋊C3 | semidirect |
| 92. C22×C7 | C3×#87704 | semidirect |
| 101. ΓL(1,𝔽8) | C22⋊#87704 | direct (N × H) |
| 102. C19 | ΓL(1,𝔽8)×C22⋊ΓL(1,𝔽8) | semidirect |
| 112. C7 | ΓL(1,𝔽8)×C22⋊(C19⋊C3) | semidirect |
| 113. C7 | C3×C22⋊#87704 | semidirect |
| 115. C22 | ΓL(1,𝔽8)×#87704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×C19×ΓL(1,𝔽8) | 3 |
| C22⋊#14584115 | 3 |
| C7×C22⋊#87704 | 3 |
| C22⋊(C19⋊#3862) | 3 |
| ΓL(1,𝔽8)×#87704 | 4 |
| C3×C22⋊#87704 | 7 |
| ΓL(1,𝔽8)×C22⋊(C19⋊C3) | 7 |
| ΓL(1,𝔽8)×C22⋊ΓL(1,𝔽8) | 19 |