Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
230 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 41 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)×#168 | C2 | semidirect |
| 3. SL(2,𝔽3)⋊#168 | C2 | semidirect |
| 11. Q8×#168 | D3 | semidirect |
| 45. C5×SL(2,𝔽3) | M16 | semidirect |
| 90. C5×Q8 | ΓL(1,𝔽25) | semidirect |
| 104. #168 | GL(2,𝔽3) | semidirect |
| 127. SL(2,𝔽3) | #681 | semidirect |
| 170. Q8 | #6650 | semidirect |
| 189. C5 | #73018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×GL(2,𝔽3) | 2 |
| SL(2,𝔽3)×#168 | 2 |
| SL(2,𝔽3)⋊#168 | 2 |
| #10601689 | 3 |
| C2×#6650 | 4 |
| #73018 | 5 |