Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
360 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. C3×#65705 | C2 | semidirect |
| 2. #11751914 | C2 | semidirect |
| 4. #11746742 | C2 | semidirect |
| 5. #11746514 | C2 | semidirect |
| 6. #11746490 | C2 | semidirect |
| 7. C3⋊C8×#170 | C2 | semidirect |
| 26. #65705 | D3 | semidirect |
| 93. C3×#170 | D8 | semidirect |
| 95. C5×C3⋊C8 | M16 | semidirect |
| 189. #170 | #213 | semidirect |
| 233. C3⋊C8 | #700 | semidirect |
| 267. C3×C5 | #1589 | semidirect |
| 314. C5 | #70859 | semidirect |
| 329. C3 | #10604067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65705 | 2 |
| #11751914 | 2 |
| #11747223 | 2 |
| #11746742 | 2 |
| #11746514 | 2 |
| #11746490 | 2 |
| C3⋊C8×#170 | 2 |
| #10604067 | 3 |
| #70859 | 5 |