Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
248 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 248 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⋊#19150296 | C2 | semidirect |
| 2. C3⋊#19150294 | C2 | semidirect |
| 3. C3×#19150284 | C2 | semidirect |
| 4. D21⋊D133 | C3 | semidirect |
| 6. C3×#14584115 | C22 | semidirect |
| 7. C7×D399 | C2×C3 | semidirect |
| 8. C7×C19×D21 | C2×C3 | semidirect |
| 9. C3×C7⋊D133 | C2×C3 | semidirect |
| 13. #19150284 | D3 | semidirect |
| 18. #14584115 | C2×D3 | semidirect |
| 19. C3×C72×C19 | C22×C3 | semidirect |
| 27. C7⋊D133 | C3×D3 | semidirect |
| 38. C72×C19 | C2×C3×D3 | semidirect |
| 42. D399 | AGL(1,𝔽7) | semidirect |
| 43. C19×D21 | AGL(1,𝔽7) | semidirect |
| 66. C3×C7×C19 | C2×AGL(1,𝔽7) | semidirect |
| 67. C3×C7×C19 | C2×AGL(1,𝔽7) | semidirect |
| 78. C7×D21 | 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 |
| 128. C3×C19 | #64423⋊C2 | semidirect |
| 131. C72 | D3×D19⋊C3 | semidirect |
| 133. D21 | #11716327 | semidirect |
| 156. C3×C7 | #11716321⋊C2 | semidirect |
| 157. C3×C7 | C2×#11716327 | semidirect |
| 164. C19 | #13183634 | semidirect |
| 179. C7 | D3×#11716327 | semidirect |
| 180. C7 | #11716327⋊D3 | semidirect |
| 191. C3 | #26013890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊#19150296 | 2 |
| C3⋊#19150294 | 2 |
| C3×#19150284 | 2 |
| D21⋊D133 | 3 |
| #26013890 | 3 |
| #11716327⋊D3 | 7 |
| D3×#11716327 | 7 |
| #13183634 | 19 |