Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 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⋊#19150317 |
| 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. C7×Dic399 | C3 | semidirect |
| 4. C3×C7×#87704 | C4 | semidirect |
| 12. C7×#87704 | Dic3 | semidirect |
| 13. C3×C72×C19 | C3×C4 | semidirect |
| 18. Dic399 | ΓL(1,𝔽8) | semidirect |
| 22. C3×#87704 | Dic7 | semidirect |
| 24. C72×C19 | C3×Dic3 | semidirect |
| 40. C3×C7×C19 | C4×ΓL(1,𝔽8) | semidirect |
| 41. C3×C7×C19 | C3×Dic7 | semidirect |
| 43. #87704 | Dic21 | semidirect |
| 59. C3×C72 | (C19⋊C3)⋊C4 | semidirect |
| 63. C7×C19 | Dic3×ΓL(1,𝔽8) | semidirect |
| 64. C7×C19 | C3×Dic21 | semidirect |
| 78. C3×C19 | ΓL(1,𝔽8)×Dic7 | semidirect |
| 81. C72 | C3⋊((C19⋊C3)⋊C4) | semidirect |
| 96. C3×C7 | (C19⋊C3)⋊Dic7 | semidirect |
| 97. C3×C7 | #13097582 | semidirect |
| 100. C19 | ΓL(1,𝔽8)×Dic21 | semidirect |
| 109. C7 | C3⋊#13097582 | semidirect |
| 110. C7 | C3⋊((C19⋊C3)⋊Dic7) | semidirect |
| 117. C3 | #26013850 | 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 |
| C7×Dic399 | 3 |
| #26013850 | 3 |
| C3⋊((C19⋊C3)⋊Dic7) | 7 |
| C3⋊#13097582 | 7 |
| ΓL(1,𝔽8)×Dic21 | 19 |