Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
440 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D3×C3⋊(C7⋊D7) |
| commutator, cosocle, hypocenter | C32×C72 | C22×C19 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C19 | C22 |
| LCS | G ▷ C32×C72 | |
| UCS | C1 ◁ C19 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×D3×C72×C19 | C2 | semidirect |
| 2. C3×C19×C3⋊(C7⋊D7) | C2 | semidirect |
| 3. C19×C3⋊(C3⋊(C7⋊D7)) | C2 | semidirect |
| 6. C32×C72×C19 | C22 | semidirect |
| 10. C19×C3⋊(C7⋊D7) | D3 | direct (N × H) |
| 11. D3×C72×C19 | D3 | semidirect |
| 17. C3×C72×C19 | C2×D3 | semidirect |
| 18. C3×C72×C19 | C2×D3 | semidirect |
| 21. C3×D3×C7×C19 | D7 | semidirect |
| 25. D3×C3⋊(C7⋊D7) | C19 | direct (N × H) |
| 28. C32×C7×C19 | C2×D7 | semidirect |
| 29. C72×C19 | D32 | semidirect |
| 30. C3⋊(C3⋊(C7⋊D7)) | C2×C19 | semidirect |
| 31. C3×C3⋊(C7⋊D7) | C2×C19 | semidirect |
| 32. C3×D3×C72 | C2×C19 | semidirect |
| 38. D3×C7×C19 | D21 | semidirect |
| 44. C32×C72 | C22×C19 | semidirect |
| 46. C3×C7×C19 | D3×D7 | semidirect |
| 47. C3×C7×C19 | C2×D21 | semidirect |
| 50. C3×D3×C19 | C7⋊D7 | semidirect |
| 55. C3⋊(C7⋊D7) | D3×C19 | direct (N × H) |
| 56. D3×C72 | D3×C19 | semidirect |
| 65. C32×C19 | C2×C7⋊D7 | semidirect |
| 67. C3×C72 | C2×D3×C19 | semidirect |
| 68. C3×C72 | C2×D3×C19 | semidirect |
| 69. C7×C19 | D3×D21 | semidirect |
| 72. C3×D3×C7 | D7×C19 | semidirect |
| 79. D3×C19 | C3⋊(C7⋊D7) | direct (N × H) |
| 86. C32×C7 | C2×D7×C19 | semidirect |
| 88. C3×C19 | D3×C7⋊D7 | semidirect |
| 89. C3×C19 | C2×C3⋊(C7⋊D7) | semidirect |
| 90. C72 | D32×C19 | semidirect |
| 97. D3×C7 | C19×D21 | semidirect |
| 104. C3×C7 | D3×D7×C19 | semidirect |
| 105. C3×C7 | C2×C19×D21 | semidirect |
| 106. C19 | D3×C3⋊(C7⋊D7) | direct (N × H) |
| 109. C3×D3 | C19×C7⋊D7 | semidirect |
| 115. C32 | C2×C19×C7⋊D7 | semidirect |
| 116. C7 | D3×C19×D21 | semidirect |
| 123. D3 | C19×C3⋊(C7⋊D7) | direct (N × H) |
| 126. C3 | D3×C19×C7⋊D7 | semidirect |
| 127. C3 | C2×C19×C3⋊(C7⋊D7) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D3×C72×C19 | 2 |
| C3×C19×C3⋊(C7⋊D7) | 2 |
| C19×C3⋊(C3⋊(C7⋊D7)) | 2 |
| C2×C19×C3⋊(C7⋊D7) | 3 |
| D3×C19×C7⋊D7 | 3 |
| D3×C19×D21 | 7 |
| D3×C3⋊(C7⋊D7) | 19 |