Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
310 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 86 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. SL(2,𝔽3)×#170 | C2 | direct (N × H) |
| 3. C2×Q8×#170 | C3 | semidirect |
| 11. Q8×#170 | C2×C3 | semidirect |
| 15. C2×C5×SL(2,𝔽3) | C8 | semidirect |
| 40. C5×SL(2,𝔽3) | C2×C8 | semidirect |
| 48. C2×C5×Q8 | C3×C8 | semidirect |
| 55. C2×#170 | SL(2,𝔽3) | direct (N × H) |
| 77. C2×SL(2,𝔽3) | #170 | direct (N × H) |
| 85. C5×Q8 | C2×C3×C8 | semidirect |
| 98. #170 | C2×SL(2,𝔽3) | direct (N × H) |
| 121. SL(2,𝔽3) | C2×#170 | direct (N × H) |
| 137. C2×Q8 | C3×#170 | semidirect |
| 161. C2×C5 | C8×SL(2,𝔽3) | semidirect |
| 169. Q8 | C2×C3×#170 | semidirect |
| 187. C5 | C2×C8×SL(2,𝔽3) | semidirect |
| 201. C2 | SL(2,𝔽3)×#170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic5×SL(2,𝔽3) | 2 |
| SL(2,𝔽3)×#170 | 2 |
| C2×Q8×#170 | 3 |
| C22×C3×#170 | 4 |
| C2×C8×SL(2,𝔽3) | 5 |