Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 110 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. #11746475 | C2 | direct (N × H) |
| 13. C2×C3⋊#672 | C4 | semidirect |
| 14. C2×C5×C3⋊C16 | C4 | semidirect |
| 15. #90934 | C4 | semidirect |
| 35. C3⋊#672 | C2×C4 | semidirect |
| 36. C5×C3⋊C16 | C2×C4 | semidirect |
| 77. C2×C3⋊C16 | AGL(1,𝔽5) | semidirect |
| 120. C3⋊C16 | C2×AGL(1,𝔽5) | semidirect |
| 146. C2×C3×C5 | #365 | semidirect |
| 188. C3×C5 | C2×#365 | semidirect |
| 198. C2×C5 | #4494 | semidirect |
| 218. C2×C3 | ΓL(1,𝔽81) | semidirect |
| 220. C5 | C2×#4494 | semidirect |
| 230. C3 | C2×ΓL(1,𝔽81) | semidirect |
| 233. C2 | #11746475 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91222 | 2 |
| C2×C3×#3995 | 2 |
| C2×#90934 | 2 |
| #11746475 | 2 |
| C2×ΓL(1,𝔽81) | 3 |
| C2×#4494 | 5 |