Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
136 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#19150306 |
| commutator, hypocenter | C3×C72×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C19 | C2×C3 |
| prime radical | C2×C3×C7×#87704 | C2 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊(C7⋊Dic133) | C3 | semidirect |
| 4. C3×C7×#87704 | C4 | semidirect |
| 12. C7×#87704 | Dic3 | semidirect |
| 13. C3×C72×C19 | C3×C4 | semidirect |
| 23. C3×#87704 | Dic7 | semidirect |
| 25. C72×C19 | C3×Dic3 | semidirect |
| 42. C3×C7×C19 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 43. C3×C7×C19 | C3×Dic7 | semidirect |
| 45. #87704 | Dic21 | semidirect |
| 61. C3×C72 | (C19⋊C3)⋊C4 | semidirect |
| 65. C7×C19 | C3⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
| 66. C7×C19 | C3×Dic21 | semidirect |
| 81. C3×C19 | ΓL(1,𝔽8)⋊Dic7 | semidirect |
| 84. C72 | C3⋊((C19⋊C3)⋊C4) | semidirect |
| 100. C3×C7 | (C19⋊C3)⋊Dic7 | semidirect |
| 101. C3×C7 | #13097588 | semidirect |
| 104. C19 | C3⋊(ΓL(1,𝔽8)⋊Dic7) | semidirect |
| 113. C7 | C3⋊#13097588 | semidirect |
| 114. C7 | C3⋊((C19⋊C3)⋊Dic7) | semidirect |
| 121. C3 | #26013839 | 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 |
| C3⋊(C7⋊Dic133) | 3 |
| #26013839 | 3 |
| C3⋊((C19⋊C3)⋊Dic7) | 7 |
| C3⋊#13097588 | 7 |
| C3⋊(ΓL(1,𝔽8)⋊Dic7) | 19 |