Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
184 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 26 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 | C1 | G |
| commutator, cosocle, hypocenter | C3×C19×#3862 | C22 |
| Fitting, socle | C3×C72×C19 | C2×D3 |
| LCS | G ▷ C3×C19×#3862 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊(C19⋊#64418) | C2 | semidirect |
| 2. C19×C3⋊#64418 | C2 | semidirect |
| 3. C3×#19150292 | C2 | semidirect |
| 6. C3×C19×#3862 | C22 | semidirect |
| 9. C3×C7⋊D133 | D3 | semidirect |
| 12. #19150292 | D3 | semidirect |
| 14. C19×#3862 | C2×D3 | semidirect |
| 15. C3×C72×C19 | C2×D3 | semidirect |
| 17. C7⋊D133 | C3⋊D3 | semidirect |
| 24. C72×C19 | C2×C3⋊D3 | semidirect |
| 27. C3⋊#64418 | D19 | semidirect |
| 41. C3×#3862 | C2×D19 | semidirect |
| 66. C3×C72 | D3×D19 | semidirect |
| 67. #3862 | D3×D19 | semidirect |
| 86. C3×C19 | #64418⋊C2 | semidirect |
| 87. C72 | C3⋊D3×D19 | semidirect |
| 106. C19 | #13183625 | semidirect |
| 131. C3 | #64418⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊(C19⋊#64418) | 2 |
| C19×C3⋊#64418 | 2 |
| C3×#19150292 | 2 |
| D21⋊D133 | 3 |
| #64418⋊D19 | 3 |
| #13183625 | 19 |
| C3⋊D3×D19 | 49 |