Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
236 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
| 14. C5×#41⋊C3 | C8 | semidirect |
| 37. C5×SL(2,𝔽3) | C2×C8 | semidirect |
| 44. C5×#41 | C3⋊C8 | semidirect |
| 70. #41⋊C3 | #168 | semidirect |
| 111. SL(2,𝔽3) | C2×#168 | semidirect |
| 126. #41 | C3⋊#168 | semidirect |
| 173. C5 | #73071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#41⋊C3 | 2 |
| SL(2,𝔽3)⋊#168 | 2 |
| #10602432 | 3 |
| C4⋊(C3⋊#168) | 4 |
| #73071 | 5 |