Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
136 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 41 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⋊(D19⋊#3862) |
| commutator, hypocenter | C3×C72×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C19 | C2×C3 |
| prime radical | C2×C3×C19⋊#3862 | 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. C72×Dic57 | C3 | semidirect |
| 4. C3×C19⋊#3862 | C4 | semidirect |
| 12. C19⋊#3862 | Dic3 | semidirect |
| 13. C3×C72×C19 | C3×C4 | semidirect |
| 19. C7×Dic57 | ΓL(1,𝔽8) | semidirect |
| 20. C7×Dic57 | ΓL(1,𝔽8) | semidirect |
| 25. C72×C19 | C3×Dic3 | semidirect |
| 42. C3×C7×C19 | C4×ΓL(1,𝔽8) | semidirect |
| 43. C3×C7×C19 | C4×ΓL(1,𝔽8) | semidirect |
| 57. Dic57 | #3862 | semidirect |
| 61. C3×C72 | (C19⋊C3)⋊C4 | semidirect |
| 65. C7×C19 | Dic3×ΓL(1,𝔽8) | semidirect |
| 66. C7×C19 | Dic3×ΓL(1,𝔽8) | semidirect |
| 81. C3×C19 | C4×#3862 | semidirect |
| 84. C72 | C3⋊((C19⋊C3)⋊C4) | semidirect |
| 98. C3×C7 | #13097582 | semidirect |
| 99. C3×C7 | #13097583 | semidirect |
| 104. C19 | Dic3×#3862 | semidirect |
| 113. C7 | C3⋊#13097582 | semidirect |
| 114. C7 | C3⋊#13097583 | semidirect |
| 121. C3 | Dic19⋊#3862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C19⋊#3862 | 2 |
| C72×Dic57 | 3 |
| Dic19⋊#3862 | 3 |
| C3⋊#13097583 | 7 |
| C3⋊#13097582 | 7 |
| Dic3×#3862 | 19 |