Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
104 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 22 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 | #30660729 |
| commutator, hypocenter | C19×#3862 | C3×C4 |
| Fitting, socle | C2×C72×C19 | C3×D3 |
| prime radical | C2×C19×ΓL(1,𝔽8)2 | C2 |
| cosocle | C2×C19×#3862 | C2×C3 |
| LCS | G ▷ C19×#3862 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C19⋊#10596868 | C3 | semidirect |
| 4. C19×ΓL(1,𝔽8)2 | C4 | semidirect |
| 9. C19×#3862 | C3×C4 | semidirect |
| 10. C19×#3861 | Dic3 | semidirect |
| 18. C72×C19 | C3×Dic3 | semidirect |
| 31. ΓL(1,𝔽8)2 | Dic19 | semidirect |
| 49. #3862 | C3×Dic19 | semidirect |
| 50. #3861 | Dic57 | semidirect |
| 67. C72 | C3×Dic57 | semidirect |
| 84. C19 | #10596868⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C19×ΓL(1,𝔽8)2 | 2 |
| C19⋊#10596868 | 3 |
| #26013831 | 3 |
| #10596868⋊C3 | 19 |
| C3×Dic57 | 49 |