Finite Group DatabasebetaFinite Group DatabasebetaOrder 3360.
272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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. #10587987⋊C3 | C2 | semidirect |
| 2. C2×C5×C4⋊AGL(1,𝔽7) | C2 | semidirect |
| 3. ΓL(1,𝔽8)×#681 | C2 | semidirect |
| 4. #10587846⋊C3 | C2 | semidirect |
| 5. #10587842⋊C3 | C2 | semidirect |
| 6. #11764811 | C3 | semidirect |
| 10. C4⋊(C5⋊AGL(1,𝔽7)) | C22 | semidirect |
| 12. Dic70⋊C3 | C22 | semidirect |
| 15. ΓL(1,𝔽8)×#168 | C22 | semidirect |
| 17. #10587987 | C2×C3 | semidirect |
| 18. C2×C5×D28 | C2×C3 | semidirect |
| 19. C7×#681 | C2×C3 | semidirect |
| 20. #10587846 | C2×C3 | semidirect |
| 21. #10587842 | C2×C3 | semidirect |
| 31. C2×C4⋊AGL(1,𝔽7) | D5 | semidirect |
| 38. D140 | C22×C3 | semidirect |
| 40. Dic70 | C22×C3 | semidirect |
| 43. C7×#168 | C22×C3 | semidirect |
| 81. C2×D28 | C3×D5 | semidirect |
| 85. C5×ΓL(1,𝔽8) | AGL(1,ℤ/8) | semidirect |
| 98. #681 | AGL(1,𝔽7) | semidirect |
| 136. #168 | C2×AGL(1,𝔽7) | semidirect |
| 137. C5×C7 | C3×AGL(1,ℤ/8) | semidirect |
| 159. ΓL(1,𝔽8) | #4078 | semidirect |
| 197. C7 | C3×#4078 | semidirect |
| 202. C5 | #6471⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10587987⋊C3 | 2 |
| C2×C5×C4⋊AGL(1,𝔽7) | 2 |
| ΓL(1,𝔽8)×#681 | 2 |
| #10587846⋊C3 | 2 |
| #10587842⋊C3 | 2 |
| #11764811 | 3 |
| #6471⋊C3 | 5 |
| C3×#4078 | 7 |