Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
184 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 36 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⋊#19150304 | C2 | semidirect |
| 2. C3×C19×#64425 | C2 | semidirect |
| 3. #26014025 | C3 | semidirect |
| 5. C3×C19×#3862 | C22 | semidirect |
| 6. C7×D399 | C2×C3 | semidirect |
| 7. C3×C19×C7⋊D7 | C2×C3 | semidirect |
| 10. C19×#64425 | D3 | semidirect |
| 14. C19×#3862 | C2×D3 | semidirect |
| 15. C3×C72×C19 | C22×C3 | semidirect |
| 19. C19×C7⋊D7 | C3×D3 | semidirect |
| 25. C72×C19 | C2×C3×D3 | semidirect |
| 27. C3×#64425 | D19 | semidirect |
| 28. D399 | AGL(1,𝔽7) | semidirect |
| 40. C3×#3862 | C2×D19 | semidirect |
| 42. C3×C7×C19 | C2×AGL(1,𝔽7) | semidirect |
| 48. C3×C7⋊D7 | C3×D19 | semidirect |
| 50. #64425 | D57 | semidirect |
| 61. C3×C72 | C2×C3×D19 | semidirect |
| 63. #3862 | C2×D57 | semidirect |
| 65. C7×C19 | D3×AGL(1,𝔽7) | semidirect |
| 74. C7⋊D7 | C3×D57 | semidirect |
| 82. C3×C19 | #64422⋊C2 | semidirect |
| 83. C72 | C2×C3×D57 | semidirect |
| 97. C3×C7 | D19×AGL(1,𝔽7) | semidirect |
| 100. C19 | #13183636 | semidirect |
| 111. C7 | AGL(1,𝔽7)×D57 | semidirect |
| 120. C3 | #26013904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊#19150304 | 2 |
| C3×C19×#64425 | 2 |
| #26014025 | 3 |
| #26013904 | 3 |
| AGL(1,𝔽7)×D57 | 7 |
| #13183636 | 19 |