Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
216 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 33 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⋊(D19⋊#3862) | C2 | semidirect |
| 2. C3⋊#19150290 | C2 | semidirect |
| 3. C3×#19150291 | C2 | semidirect |
| 4. C7⋊D7×D57 | C3 | semidirect |
| 6. C3×C19⋊#3862 | C22 | semidirect |
| 7. C3⋊(C7⋊D133) | C2×C3 | semidirect |
| 8. C72×D57 | C2×C3 | semidirect |
| 9. C3×C19×C7⋊D7 | C2×C3 | semidirect |
| 12. #19150291 | D3 | semidirect |
| 18. C19⋊#3862 | C2×D3 | semidirect |
| 19. C3×C72×C19 | C22×C3 | semidirect |
| 27. C19×C7⋊D7 | C3×D3 | semidirect |
| 37. C72×C19 | C2×C3×D3 | semidirect |
| 45. C7×D57 | AGL(1,𝔽7) | semidirect |
| 46. C7×D57 | AGL(1,𝔽7) | semidirect |
| 66. C3×C7×C19 | C2×AGL(1,𝔽7) | semidirect |
| 67. C3×C7×C19 | C2×AGL(1,𝔽7) | semidirect |
| 77. C3×C7⋊D7 | D19⋊C3 | semidirect |
| 97. C3×C72 | C2×D19⋊C3 | semidirect |
| 101. C7×C19 | D3×AGL(1,𝔽7) | semidirect |
| 102. C7×C19 | D3×AGL(1,𝔽7) | semidirect |
| 111. D57 | #64425 | semidirect |
| 118. C7⋊D7 | C3⋊(D19⋊C3) | semidirect |
| 127. C3×C19 | C2×#64425 | semidirect |
| 130. C72 | C2×C3⋊(D19⋊C3) | semidirect |
| 156. C3×C7 | #11716321⋊C2 | semidirect |
| 157. C3×C7 | #11716322⋊C2 | semidirect |
| 162. C19 | D3×#64425 | semidirect |
| 179. C7 | #11716325⋊D3 | semidirect |
| 180. C7 | #11716326⋊D3 | semidirect |
| 191. C3 | D19⋊#64425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊(D19⋊#3862) | 2 |
| C3⋊#19150290 | 2 |
| C3×#19150291 | 2 |
| C7⋊D7×D57 | 3 |
| D19⋊#64425 | 3 |
| #11716326⋊D3 | 7 |
| #11716325⋊D3 | 7 |
| D3×#64425 | 19 |