Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
120 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 46 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. C7×C19×Dic21 | C3 | semidirect |
| 4. C3×C7×#87705 | C4 | semidirect |
| 8. C3⋊#13097587 | C7 | direct (N × H) |
| 12. C7×#87705 | Dic3 | semidirect |
| 13. C3×C72×C19 | C3×C4 | semidirect |
| 18. C19×Dic21 | C3×C7 | semidirect |
| 22. C3×#87705 | C4×C7 | semidirect |
| 24. C72×C19 | C3×Dic3 | semidirect |
| 34. C7×Dic21 | C19⋊C3 | semidirect |
| 40. C3×C7×C19 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 41. C3×C7×C19 | C3×C4×C7 | semidirect |
| 43. #87705 | C7×Dic3 | semidirect |
| 59. C3×C72 | C4×C19⋊C3 | semidirect |
| 63. C7×C19 | C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 64. C7×C19 | C3×C7×Dic3 | semidirect |
| 72. Dic21 | C7×C19⋊C3 | semidirect |
| 78. C3×C19 | C7×ΓL(1,𝔽8)⋊C4 | semidirect |
| 81. C72 | Dic3×C19⋊C3 | semidirect |
| 96. C3×C7 | #13097587 | semidirect |
| 97. C3×C7 | C4×C7×C19⋊C3 | semidirect |
| 100. C19 | C7×C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 109. C7 | C7×Dic3×C19⋊C3 | semidirect |
| 110. C7 | C3⋊#13097587 | direct (N × H) |
| 117. C3 | C7×#13097587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×#87705 | 2 |
| C7×C19×Dic21 | 3 |
| C7×#13097587 | 3 |
| C3⋊#13097587 | 7 |
| C7×Dic3×C19⋊C3 | 7 |
| C7×C3⋊(ΓL(1,𝔽8)⋊C4) | 19 |