Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
302 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 92 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. C5×SL(2,𝔽3)⋊C8 | C2 | direct (N × H) |
| 8. C2×SL(2,𝔽3)⋊C8 | C5 | direct (N × H) |
| 15. C2×C5×SL(2,𝔽3) | C8 | semidirect |
| 20. SL(2,𝔽3)⋊C8 | C2×C5 | direct (N × H) |
| 40. C5×SL(2,𝔽3) | C2×C8 | semidirect |
| 48. C2×C5×Q8 | C3⋊C8 | semidirect |
| 77. C2×SL(2,𝔽3) | C5×C8 | semidirect |
| 85. C5×Q8 | C2×C3⋊C8 | semidirect |
| 121. SL(2,𝔽3) | C2×C5×C8 | semidirect |
| 137. C2×Q8 | C5×C3⋊C8 | semidirect |
| 161. C2×C5 | SL(2,𝔽3)⋊C8 | direct (N × H) |
| 169. Q8 | C2×C5×C3⋊C8 | semidirect |
| 187. C5 | C2×SL(2,𝔽3)⋊C8 | direct (N × H) |
| 201. C2 | C5×SL(2,𝔽3)⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×SL(2,𝔽3) | 2 |
| C5×SL(2,𝔽3)⋊C8 | 2 |
| C2×C5×Q8⋊C8 | 3 |
| C22×C5×C3⋊C8 | 4 |
| C2×SL(2,𝔽3)⋊C8 | 5 |