Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
248 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 37 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, Fitting, socle, cosocle, hypocenter | C3×C72×C19 | C22×C3 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊#19150297 | C2 | semidirect |
| 2. C3×#19150287 | C2 | semidirect |
| 3. C19×D21⋊D7 | C3 | semidirect |
| 5. C3×#14584116 | C22 | semidirect |
| 6. C7×C19×D21 | C2×C3 | semidirect |
| 7. C3×C19×C7⋊D7 | C2×C3 | semidirect |
| 10. #19150287 | D3 | semidirect |
| 14. #14584116 | C2×D3 | semidirect |
| 15. C3×C72×C19 | C22×C3 | semidirect |
| 20. C19×C7⋊D7 | C3×D3 | semidirect |
| 27. C72×C19 | C2×C3×D3 | semidirect |
| 30. C19×D21 | AGL(1,𝔽7) | semidirect |
| 41. D21⋊D7 | C19⋊C3 | semidirect |
| 46. C3×C7×C19 | C2×AGL(1,𝔽7) | semidirect |
| 53. C7×D21 | C2×C19⋊C3 | semidirect |
| 54. C3×C7⋊D7 | C2×C19⋊C3 | semidirect |
| 67. C3×C72 | C22×C19⋊C3 | semidirect |
| 71. C7×C19 | D3×AGL(1,𝔽7) | semidirect |
| 81. C7⋊D7 | D3×C19⋊C3 | semidirect |
| 88. C3×C19 | #64423⋊C2 | semidirect |
| 91. C72 | C2×D3×C19⋊C3 | semidirect |
| 92. D21 | #11716326 | semidirect |
| 107. C3×C7 | C2×#11716326 | semidirect |
| 112. C19 | #13183634 | semidirect |
| 123. C7 | D3×#11716326 | semidirect |
| 132. C3 | #26013895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊#19150297 | 2 |
| C3×#19150287 | 2 |
| C19×D21⋊D7 | 3 |
| #26013895 | 3 |
| D3×#11716326 | 7 |
| #13183634 | 19 |