Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
284 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 2. C3×#65739 | C2 | semidirect |
| 4. C3×#64910 | C2 | semidirect |
| 6. C3×ΓL(1,𝔽81) | C2 | semidirect |
| 7. C3×#64845 | C2 | semidirect |
| 8. #10604138 | C3 | direct (N × H) |
| 19. C3×C5×Q32 | C4 | semidirect |
| 20. C3×#3961 | C4 | semidirect |
| 21. C3×#3960 | C4 | semidirect |
| 22. C3×#3932 | C4 | semidirect |
| 26. #65739 | C2×C3 | semidirect |
| 28. #64910 | C2×C3 | semidirect |
| 30. ΓL(1,𝔽81) | C2×C3 | semidirect |
| 31. #64845 | C2×C3 | semidirect |
| 69. C5×Q32 | C3×C4 | semidirect |
| 70. #3961 | C3×C4 | semidirect |
| 71. #3960 | C3×C4 | semidirect |
| 72. #3932 | C3×C4 | semidirect |
| 95. C3×Q32 | AGL(1,𝔽5) | semidirect |
| 181. Q32 | C3×AGL(1,𝔽5) | semidirect |
| 238. C3×C5 | #2180 | semidirect |
| 269. C5 | C3×#2180 | semidirect |
| 279. C3 | #10604138 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65741 | 2 |
| C3×#65739 | 2 |
| C3×#65207 | 2 |
| C3×#64910 | 2 |
| C3×#64907 | 2 |
| C3×ΓL(1,𝔽81) | 2 |
| C3×#64845 | 2 |
| #10604138 | 3 |
| C3×#2180 | 5 |