Finite Group DatabasebetaFinite Group DatabasebetaOrder 23940.
240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D35⋊D19 |
| commutator, cosocle, hypocenter | C5×C7×C19 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C19 | C22 |
| LCS | G ▷ C5×C7×C19 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C5×D133 | C2 | semidirect |
| 2. C32×C7×D95 | C2 | semidirect |
| 3. C32×C19×D35 | C2 | semidirect |
| 4. C3×D35⋊D19 | C3 | direct (N × H) |
| 5. C32×C5×C7×C19 | C22 | semidirect |
| 7. C3×C19×D35 | C2×C3 | semidirect |
| 8. C3×C7×D95 | C2×C3 | semidirect |
| 9. C3×C5×D133 | C2×C3 | semidirect |
| 11. D35⋊D19 | C32 | direct (N × H) |
| 12. C32×D133 | D5 | semidirect |
| 15. C3×C5×C7×C19 | C22×C3 | semidirect |
| 16. C32×D95 | D7 | semidirect |
| 20. C19×D35 | C2×C32 | semidirect |
| 21. C7×D95 | C2×C32 | semidirect |
| 22. C5×D133 | C2×C32 | semidirect |
| 24. C32×C7×C19 | C2×D5 | semidirect |
| 26. C32×C5×C19 | C2×D7 | semidirect |
| 27. C3×D133 | C3×D5 | semidirect |
| 31. C5×C7×C19 | C22×C32 | semidirect |
| 32. C32×D35 | D19 | semidirect |
| 35. C3×D95 | C3×D7 | semidirect |
| 40. C3×C7×C19 | C2×C3×D5 | semidirect |
| 45. C32×C5×C7 | C2×D19 | semidirect |
| 46. C3×C5×C19 | C2×C3×D7 | semidirect |
| 47. D133 | C32×D5 | semidirect |
| 52. C3×D35 | C3×D19 | semidirect |
| 55. D95 | C32×D7 | semidirect |
| 59. C32×C19 | D5×D7 | semidirect |
| 61. C7×C19 | C2×C32×D5 | semidirect |
| 68. C3×C5×C7 | C2×C3×D19 | semidirect |
| 69. C5×C19 | C2×C32×D7 | semidirect |
| 75. D35 | C32×D19 | semidirect |
| 78. C32×C7 | D5×D19 | semidirect |
| 80. C3×C19 | C3×D5×D7 | semidirect |
| 81. C32×C5 | D7×D19 | semidirect |
| 89. C5×C7 | C2×C32×D19 | semidirect |
| 94. C3×C7 | C3×D5×D19 | semidirect |
| 96. C19 | C32×D5×D7 | semidirect |
| 100. C3×C5 | C3×D7×D19 | semidirect |
| 108. C32 | D35⋊D19 | direct (N × H) |
| 109. C7 | C32×D5×D19 | semidirect |
| 113. C5 | C32×D7×D19 | semidirect |
| 115. C3 | C3×D35⋊D19 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×D133 | 2 |
| C32×C7×D95 | 2 |
| C32×C19×D35 | 2 |
| C3×D35⋊D19 | 3 |
| C32×D7×D19 | 5 |
| C32×D5×D19 | 7 |
| C32×D5×D7 | 19 |