Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
216 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 35 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. D57×#3862 | C2 | semidirect |
| 2. C19×C3⋊#64425 | C2 | semidirect |
| 3. C3×#19150292 | C2 | semidirect |
| 4. D57⋊(C7⋊D7) | C3 | semidirect |
| 6. C3×C19×#3862 | C22 | semidirect |
| 7. C19×C3⋊(C7⋊D7) | C2×C3 | semidirect |
| 8. C72×D57 | C2×C3 | semidirect |
| 9. C3×C7⋊D133 | C2×C3 | semidirect |
| 12. #19150292 | D3 | semidirect |
| 17. C19×#3862 | C2×D3 | semidirect |
| 18. C3×C72×C19 | C22×C3 | semidirect |
| 22. C7⋊D133 | C3×D3 | semidirect |
| 30. C72×C19 | C2×C3×D3 | semidirect |
| 31. C3⋊#64425 | D19 | semidirect |
| 37. C7×D57 | AGL(1,𝔽7) | semidirect |
| 49. C3×#3862 | C2×D19 | semidirect |
| 51. C3×C7×C19 | C2×AGL(1,𝔽7) | semidirect |
| 57. C3⋊(C7⋊D7) | C3×D19 | semidirect |
| 75. C3×C72 | C2×C3×D19 | semidirect |
| 77. #3862 | D3×D19 | semidirect |
| 79. C7×C19 | D3×AGL(1,𝔽7) | semidirect |
| 84. D57 | #64425 | semidirect |
| 100. C3×C19 | C2×#64425 | semidirect |
| 101. C72 | C3×D3×D19 | semidirect |
| 119. C3×C7 | D19×AGL(1,𝔽7) | semidirect |
| 122. C19 | D3×#64425 | semidirect |
| 136. C7 | (C3⋊AGL(1,𝔽7))⋊D19 | semidirect |
| 147. C3 | D19×#64425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D57×#3862 | 2 |
| C19×C3⋊#64425 | 2 |
| C3×#19150292 | 2 |
| D57⋊(C7⋊D7) | 3 |
| D19×#64425 | 3 |
| (C3⋊AGL(1,𝔽7))⋊D19 | 7 |
| D3×#64425 | 19 |