Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 4. #11746719 | C2 | semidirect |
| 5. C3×ΓL(1,𝔽81) | C2 | semidirect |
| 6. #11746475 | C2 | semidirect |
| 7. #11746472 | C2 | semidirect |
| 18. C16×D15 | C4 | semidirect |
| 19. C5×#798 | C4 | semidirect |
| 21. #90935 | C4 | semidirect |
| 23. #90933 | C4 | semidirect |
| 29. ΓL(1,𝔽81) | D3 | semidirect |
| 47. C3×C5×C16 | C2×C4 | semidirect |
| 48. C3⋊#672 | C2×C4 | semidirect |
| 49. C3×#672 | C2×C4 | semidirect |
| 50. C5×C3⋊C16 | C2×C4 | semidirect |
| 102. #798 | AGL(1,𝔽5) | semidirect |
| 121. C5×C16 | C4×D3 | semidirect |
| 123. #672 | C4×D3 | semidirect |
| 157. C3×C16 | C2×AGL(1,𝔽5) | semidirect |
| 159. C3⋊C16 | C2×AGL(1,𝔽5) | semidirect |
| 192. D15 | #365 | semidirect |
| 239. C16 | D3×AGL(1,𝔽5) | semidirect |
| 240. C3×C5 | C2×#365 | semidirect |
| 275. C5 | D3×#365 | semidirect |
| 286. C3 | D5⋊#365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751677 | 2 |
| D3×#3993 | 2 |
| #11746809 | 2 |
| #11746719 | 2 |
| C3×ΓL(1,𝔽81) | 2 |
| #11746475 | 2 |
| #11746472 | 2 |
| D5⋊#365 | 3 |
| D3×#365 | 5 |