Finite Group DatabasebetaFinite Group Databasebeta← C3×ΓL(1,𝔽16)×ΓL(1,𝔽32) #42124709
Order 27900.
124 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. ΓL(1,𝔽16)×ΓL(1,𝔽32) | C3 | direct (N × H) |
| 4. C32×C5×ΓL(1,𝔽32) | C4 | semidirect |
| 5. C3×C31×ΓL(1,𝔽16) | C5 | semidirect |
| 14. C3×C5×ΓL(1,𝔽32) | Dic3 | semidirect |
| 15. C3×C5×ΓL(1,𝔽32) | C3×C4 | semidirect |
| 16. C31×ΓL(1,𝔽16) | C3×C5 | semidirect |
| 21. C32×C5×C31 | C4×C5 | semidirect |
| 23. C32×ΓL(1,𝔽32) | AGL(1,𝔽5) | semidirect |
| 32. C5×ΓL(1,𝔽32) | C3×Dic3 | semidirect |
| 37. C3×C5×C31 | C5×Dic3 | semidirect |
| 38. C3×C5×C31 | C3×C4×C5 | semidirect |
| 43. C3×ΓL(1,𝔽32) | C3×AGL(1,𝔽5) | semidirect |
| 44. C3×ΓL(1,𝔽32) | ΓL(1,𝔽16) | direct (N × H) |
| 52. C32×C31 | C5×AGL(1,𝔽5) | semidirect |
| 57. C3×ΓL(1,𝔽16) | ΓL(1,𝔽32) | direct (N × H) |
| 59. C5×C31 | C3×C5×Dic3 | semidirect |
| 61. ΓL(1,𝔽32) | C3×ΓL(1,𝔽16) | direct (N × H) |
| 68. C3×C31 | C3×C5×AGL(1,𝔽5) | semidirect |
| 69. C3×C31 | C5×ΓL(1,𝔽16) | semidirect |
| 76. ΓL(1,𝔽16) | C3×ΓL(1,𝔽32) | direct (N × H) |
| 83. C32×C5 | C4×ΓL(1,𝔽32) | semidirect |
| 85. C31 | C3×C5×ΓL(1,𝔽16) | semidirect |
| 103. C3×C5 | Dic3×ΓL(1,𝔽32) | semidirect |
| 104. C3×C5 | C3×C4×ΓL(1,𝔽32) | semidirect |
| 109. C32 | AGL(1,𝔽5)×ΓL(1,𝔽32) | semidirect |
| 115. C5 | C3×Dic3×ΓL(1,𝔽32) | semidirect |
| 118. C3 | C3×AGL(1,𝔽5)×ΓL(1,𝔽32) | semidirect |
| 119. C3 | ΓL(1,𝔽16)×ΓL(1,𝔽32) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×D5×ΓL(1,𝔽32) | 2 |
| ΓL(1,𝔽16)×ΓL(1,𝔽32) | 3 |
| C3×AGL(1,𝔽5)×ΓL(1,𝔽32) | 3 |
| C3×C31×ΓL(1,𝔽16) | 5 |
| C3×Dic3×ΓL(1,𝔽32) | 5 |
| C3×C5×ΓL(1,𝔽16) | 31 |