Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
230 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D21×D133 |
| commutator, cosocle, hypocenter | C3×C72×C19 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C19 | C22 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C7×D133 | C2 | semidirect |
| 2. C3×C7×C19×D21 | C2 | semidirect |
| 3. C3×C3⋊(C7⋊D133) | C2 | semidirect |
| 4. D21×D133 | C3 | direct (N × H) |
| 6. C32×C72×C19 | C22 | semidirect |
| 7. C3⋊(C7⋊D133) | C2×C3 | semidirect |
| 8. C7×C19×D21 | C2×C3 | semidirect |
| 11. C3×C7×D133 | D3 | semidirect |
| 12. C3×C7×D133 | C2×C3 | semidirect |
| 18. C3×C72×C19 | C2×D3 | semidirect |
| 19. C3×C72×C19 | C22×C3 | semidirect |
| 23. C3×C19×D21 | D7 | semidirect |
| 25. C32×D133 | D7 | semidirect |
| 28. C7×D133 | C3×D3 | semidirect |
| 36. C32×C7×C19 | C2×D7 | semidirect |
| 37. C32×C7×C19 | C2×D7 | semidirect |
| 38. C72×C19 | C2×C3×D3 | semidirect |
| 40. C3×C7×D21 | D19 | semidirect |
| 46. C19×D21 | C3×D7 | semidirect |
| 52. C3×D133 | C3×D7 | semidirect |
| 53. C3×D133 | D21 | direct (N × H) |
| 63. C32×C72 | C2×D19 | semidirect |
| 69. C3×C7×C19 | D3×D7 | semidirect |
| 70. C3×C7×C19 | C2×C3×D7 | semidirect |
| 71. C3×C7×C19 | C2×C3×D7 | semidirect |
| 72. C3×C7×C19 | C2×D21 | semidirect |
| 77. C7×D21 | C3×D19 | semidirect |
| 87. D133 | C3×D21 | direct (N × H) |
| 95. C32×C19 | D72 | semidirect |
| 97. C3×C72 | D3×D19 | semidirect |
| 98. C3×C72 | C2×C3×D19 | semidirect |
| 100. C7×C19 | C3×D3×D7 | semidirect |
| 101. C7×C19 | C2×C3×D21 | semidirect |
| 106. C3×D21 | D133 | direct (N × H) |
| 125. C32×C7 | D7×D19 | semidirect |
| 126. C32×C7 | C2×D133 | semidirect |
| 128. C3×C19 | C3×D72 | semidirect |
| 129. C3×C19 | D7×D21 | semidirect |
| 130. C72 | C3×D3×D19 | semidirect |
| 138. D21 | C3×D133 | direct (N × H) |
| 158. C3×C7 | C3×D7×D19 | semidirect |
| 159. C3×C7 | D19×D21 | semidirect |
| 160. C3×C7 | D3×D133 | semidirect |
| 161. C3×C7 | C2×C3×D133 | semidirect |
| 162. C19 | C3×D7×D21 | semidirect |
| 175. C32 | D7×D133 | semidirect |
| 177. C7 | C3×D19×D21 | semidirect |
| 178. C7 | C3×D3×D133 | semidirect |
| 188. C3 | C3×D7×D133 | semidirect |
| 189. C3 | D21×D133 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C7×D133 | 2 |
| C3×C7×C19×D21 | 2 |
| C3×C3⋊(C7⋊D133) | 2 |
| D21×D133 | 3 |
| C3×D7×D133 | 3 |
| C3×D3×D133 | 7 |
| C3×D19×D21 | 7 |
| C3×D7×D21 | 19 |