Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
428 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 120 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. C3×#64969 | C2 | semidirect |
| 4. #11746947 | C2 | semidirect |
| 5. C8×C3⋊#168 | C2 | semidirect |
| 20. #64969 | D3 | semidirect |
| 58. C3×C5×C8 | SD16 | semidirect |
| 59. C3⋊#168 | SD16 | semidirect |
| 114. C5×C8 | #215 | semidirect |
| 137. C3×C8 | #687 | semidirect |
| 158. C3×C5 | #1705 | semidirect |
| 179. C8 | #6656 | semidirect |
| 183. C5 | #71332 | semidirect |
| 191. C3 | #10602047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4693 | 2 |
| C3×#64969 | 2 |
| #11747081 | 2 |
| #11746947 | 2 |
| C8×C3⋊#168 | 2 |
| #10602047 | 3 |
| #71332 | 5 |