Finite Group DatabasebetaFinite Group DatabasebetaOrder 33300.
224 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 50 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 | D15⋊D185 |
| commutator, cosocle, hypocenter | C3×C52×C37 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C37 | C22 |
| LCS | G ▷ C3×C52×C37 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C5⋊D185 | C2 | semidirect |
| 2. C3×C5×D15×C37 | C2 | semidirect |
| 3. C3×C5×D555 | C2 | semidirect |
| 4. D15⋊D185 | C3 | direct (N × H) |
| 6. C32×C52×C37 | C22 | semidirect |
| 9. C5×D555 | C2×C3 | semidirect |
| 10. C5×D15×C37 | C2×C3 | semidirect |
| 12. C3×C5⋊D185 | D3 | semidirect |
| 13. C3×C5⋊D185 | C2×C3 | semidirect |
| 17. C3×D555 | D5 | semidirect |
| 18. C3×D15×C37 | D5 | semidirect |
| 25. C3×C52×C37 | C2×D3 | semidirect |
| 26. C3×C52×C37 | C22×C3 | semidirect |
| 31. C5⋊D185 | C3×D3 | semidirect |
| 35. C32×C5×C37 | C2×D5 | semidirect |
| 36. C32×C5×C37 | C2×D5 | semidirect |
| 39. D555 | C3×D5 | semidirect |
| 40. D15×C37 | C3×D5 | semidirect |
| 55. C52×C37 | C2×C3×D3 | semidirect |
| 67. C3×C5×C37 | D3×D5 | semidirect |
| 68. C3×C5×C37 | D3×D5 | semidirect |
| 69. C3×C5×C37 | C2×C3×D5 | semidirect |
| 70. C3×C5×C37 | C2×C3×D5 | semidirect |
| 72. C3×C5×D15 | D37 | semidirect |
| 83. C32×C37 | D52 | semidirect |
| 86. C32×C52 | C2×D37 | semidirect |
| 95. C5×C37 | C3×D3×D5 | semidirect |
| 96. C5×C37 | C3×D3×D5 | semidirect |
| 100. C5×D15 | C3×D37 | semidirect |
| 108. C3×C37 | C3×D52 | semidirect |
| 109. C3×C37 | D15⋊D5 | semidirect |
| 112. C3×D15 | D185 | semidirect |
| 119. C3×C52 | D3×D37 | semidirect |
| 120. C3×C52 | C2×C3×D37 | semidirect |
| 132. C32×C5 | D5×D37 | semidirect |
| 133. C32×C5 | C2×D185 | semidirect |
| 134. C37 | C3×D15⋊D5 | semidirect |
| 139. D15 | C3×D185 | semidirect |
| 153. C52 | C3×D3×D37 | semidirect |
| 164. C3×C5 | C3×D5×D37 | semidirect |
| 165. C3×C5 | D3×D185 | semidirect |
| 166. C3×C5 | D15⋊D37 | semidirect |
| 167. C3×C5 | C2×C3×D185 | semidirect |
| 177. C32 | D5×D185 | semidirect |
| 186. C5 | C3×D3×D185 | semidirect |
| 187. C5 | C3×D15⋊D37 | semidirect |
| 190. C3 | C3×D5×D185 | semidirect |
| 191. C3 | D15⋊D185 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5⋊D185 | 2 |
| C3×C5×D15×C37 | 2 |
| C3×C5×D555 | 2 |
| D15⋊D185 | 3 |
| C3×D5×D185 | 3 |
| C3×D15⋊D37 | 5 |
| C3×D3×D185 | 5 |
| C3×D15⋊D5 | 37 |