Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
230 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 32 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⋊#19150295 | C2 | semidirect |
| 2. C3⋊#19150287 | C2 | semidirect |
| 3. C3×#19150295 | C2 | semidirect |
| 4. D133⋊D21 | C3 | semidirect |
| 6. C3×#14584116 | C22 | semidirect |
| 7. C19×C3⋊(C7⋊D7) | C2×C3 | semidirect |
| 8. C7×D399 | C2×C3 | semidirect |
| 9. C3×C7×D133 | C2×C3 | semidirect |
| 12. #19150295 | D3 | semidirect |
| 18. #14584116 | C2×D3 | semidirect |
| 19. C3×C72×C19 | C22×C3 | semidirect |
| 29. C7×D133 | C3×D3 | semidirect |
| 38. C72×C19 | C2×C3×D3 | semidirect |
| 42. D399 | AGL(1,𝔽7) | semidirect |
| 47. C3×D133 | AGL(1,𝔽7) | semidirect |
| 65. C3×C7×C19 | C2×AGL(1,𝔽7) | semidirect |
| 66. C3×C7×C19 | C2×AGL(1,𝔽7) | semidirect |
| 76. C3⋊(C7⋊D7) | D19⋊C3 | semidirect |
| 84. D133 | C3⋊AGL(1,𝔽7) | semidirect |
| 96. C3×C72 | C2×D19⋊C3 | semidirect |
| 100. C7×C19 | D3×AGL(1,𝔽7) | semidirect |
| 101. C7×C19 | C2×C3⋊AGL(1,𝔽7) | semidirect |
| 127. C3×C19 | #64423⋊C2 | semidirect |
| 130. C72 | D3×D19⋊C3 | semidirect |
| 154. C3×C7 | #11716322⋊C2 | semidirect |
| 155. C3×C7 | #11716322⋊C2 | semidirect |
| 162. C19 | #64423⋊D3 | semidirect |
| 177. C7 | #11716322⋊D3 | semidirect |
| 178. C7 | #11716328⋊D3 | semidirect |
| 189. C3 | #26013893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊#19150295 | 2 |
| C3⋊#19150287 | 2 |
| C3×#19150295 | 2 |
| D133⋊D21 | 3 |
| #26013893 | 3 |
| #11716328⋊D3 | 7 |
| #11716322⋊D3 | 7 |
| #64423⋊D3 | 19 |