Finite Group DatabasebetaFinite Group DatabasebetaOrder 3402.
920 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 455 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13133671 | C2 | semidirect |
| 2. C3×D7×3−1+2 | C3 | semidirect |
| 4. C3×#4430⋊C2 | C3 | semidirect |
| 5. #10588065⋊C2 | C3 | semidirect |
| 6. 3−1+2×AGL(1,𝔽7) | C3 | semidirect |
| 7. #11765710 | C3 | semidirect |
| 8. C3×C7×3−1+2 | C2×C3 | semidirect |
| 10. C3×#4430 | C2×C3 | semidirect |
| 11. #10588065 | C2×C3 | semidirect |
| 12. ΓL(1,𝔽8)×3−1+2 | C2×C3 | semidirect |
| 13. #10588061 | C2×C3 | semidirect |
| 18. D7×3−1+2 | C32 | semidirect |
| 19. C3×C9×D7 | C32 | semidirect |
| 23. #4430⋊C2 | C32 | semidirect |
| 24. #4430⋊C2 | C32 | semidirect |
| 25. C3×D7⋊C9 | C32 | semidirect |
| 26. #67356 | C32 | semidirect |
| 27. #67355 | C32 | semidirect |
| 28. C9×AGL(1,𝔽7) | C32 | semidirect |
| 33. C7×3−1+2 | C2×C32 | semidirect |
| 34. C3×C7×C9 | C2×C32 | semidirect |
| 38. #4430 | C2×C32 | semidirect |
| 39. #4430 | C2×C32 | semidirect |
| 40. C3×C7⋊C9 | C2×C32 | semidirect |
| 41. #4428 | C2×C32 | semidirect |
| 42. #4427 | C2×C32 | semidirect |
| 43. C9×ΓL(1,𝔽8) | C2×C32 | semidirect |
| 62. C3×3−1+2 | AGL(1,𝔽7) | semidirect |
| 99. 3−1+2 | C3×AGL(1,𝔽7) | semidirect |
| 104. C3×C9 | C3×AGL(1,𝔽7) | semidirect |
| 118. D7 | 3−1+4 | semidirect |
| 127. C7 | C2×3−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13133671 | 2 |
| C3×D7×3−1+2 | 3 |
| C3×D7⋊H(3,𝔽3) | 3 |
| C3×#4430⋊C2 | 3 |
| #10588065⋊C2 | 3 |
| 3−1+2×AGL(1,𝔽7) | 3 |
| #11765710 | 3 |
| C2×3−1+4 | 7 |