Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
140 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 98 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. #10597991 | C3 | direct (N × H) |
| 16. C3×C5×C16 | C8 | semidirect |
| 40. C5×C16 | C3×C8 | semidirect |
| 54. C3×C16 | #168 | semidirect |
| 87. C16 | C3×#168 | semidirect |
| 88. C3×C5 | #1371 | semidirect |
| 108. C5 | C3×#1371 | semidirect |
| 115. C3 | #10597991 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×C16 | 2 |
| C3×#64678 | 2 |
| #10597991 | 3 |
| C3×#1371 | 5 |