Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
136 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 136 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. C72×Dic57 | C3 | semidirect |
| 4. C3×C7×#87704 | C4 | semidirect |
| 8. C3⋊#13097582 | C7 | direct (N × H) |
| 12. C7×#87704 | Dic3 | semidirect |
| 13. C3×C72×C19 | C3×C4 | semidirect |
| 19. C7×Dic57 | ΓL(1,𝔽8) | semidirect |
| 20. C7×Dic57 | C3×C7 | semidirect |
| 23. C3×#87704 | C4×C7 | semidirect |
| 25. C72×C19 | C3×Dic3 | semidirect |
| 42. C3×C7×C19 | C4×ΓL(1,𝔽8) | semidirect |
| 43. C3×C7×C19 | C3×C4×C7 | semidirect |
| 45. #87704 | C7×Dic3 | semidirect |
| 57. Dic57 | C7×ΓL(1,𝔽8) | semidirect |
| 61. C3×C72 | (C19⋊C3)⋊C4 | semidirect |
| 65. C7×C19 | Dic3×ΓL(1,𝔽8) | semidirect |
| 66. C7×C19 | C3×C7×Dic3 | semidirect |
| 81. C3×C19 | C4×C7×ΓL(1,𝔽8) | semidirect |
| 84. C72 | C3⋊((C19⋊C3)⋊C4) | semidirect |
| 100. C3×C7 | C7×(C19⋊C3)⋊C4 | semidirect |
| 101. C3×C7 | #13097582 | semidirect |
| 104. C19 | C7×Dic3×ΓL(1,𝔽8) | semidirect |
| 113. C7 | C7×C3⋊((C19⋊C3)⋊C4) | semidirect |
| 114. C7 | C3⋊#13097582 | direct (N × H) |
| 121. C3 | C7×#13097582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×#87704 | 2 |
| C72×Dic57 | 3 |
| C7×#13097582 | 3 |
| C3⋊#13097582 | 7 |
| C7×C3⋊((C19⋊C3)⋊C4) | 7 |
| C7×Dic3×ΓL(1,𝔽8) | 19 |