Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
152 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 3. #10598525 | C3 | direct (N × H) |
| 31. C3×#168 | C16 | semidirect |
| 66. #168 | C3×C16 | semidirect |
| 98. C3×C5 | #1370 | semidirect |
| 120. C5 | C3×#1370 | semidirect |
| 127. C3 | #10598525 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4⋊#674 | 2 |
| C3×C8×#168 | 2 |
| #10598525 | 3 |
| C3×#1370 | 5 |