Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
146 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #64418⋊D3 |
| commutator, cosocle, hypocenter | C3×#3862 | C22×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | C2×D3 |
| LCS | G ▷ C3×#3862 | |
| UCS | C1 ◁ C19 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×C3⋊#64418 | C2 | semidirect |
| 2. C19×C3⋊#64425 | C2 | semidirect |
| 3. C3×C19×#64418 | C2 | semidirect |
| 6. C3×C19×#3862 | C22 | semidirect |
| 7. C19×C3⋊(C7⋊D7) | D3 | semidirect |
| 12. C19×#64418 | D3 | semidirect |
| 16. C19×#3862 | C2×D3 | semidirect |
| 17. C3×C72×C19 | C2×D3 | semidirect |
| 22. #64418⋊D3 | C19 | direct (N × H) |
| 26. C72×C19 | D32 | semidirect |
| 27. C3⋊#64425 | C2×C19 | semidirect |
| 28. C3⋊#64418 | C2×C19 | semidirect |
| 29. C3×#64418 | C2×C19 | semidirect |
| 43. C3×#3862 | C22×C19 | semidirect |
| 52. C3⋊(C7⋊D7) | D3×C19 | semidirect |
| 58. #64418 | D3×C19 | semidirect |
| 70. C3×C72 | C2×D3×C19 | semidirect |
| 72. #3862 | C2×D3×C19 | semidirect |
| 93. C3×C19 | #64418⋊C2 | semidirect |
| 94. C72 | D32×C19 | semidirect |
| 114. C19 | #64418⋊D3 | direct (N × H) |
| 141. C3 | C19×#64418⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×C3⋊#64418 | 2 |
| C19×C3⋊#64425 | 2 |
| C3×C19×#64418 | 2 |
| D7×C19×D21 | 3 |
| C19×#64418⋊C2 | 3 |
| #64418⋊D3 | 19 |
| D32×C19 | 49 |