Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 88 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×#65774 | C2 | semidirect |
| 2. #11751893 | C2 | semidirect |
| 4. D4⋊(C3⋊#170) | C2 | semidirect |
| 5. #11746514 | C2 | semidirect |
| 6. #11746490 | C2 | semidirect |
| 7. #170⋊(C3⋊C8) | C2 | semidirect |
| 25. #65774 | D3 | semidirect |
| 80. D60 | M16 | semidirect |
| 93. C3×#170 | D8 | semidirect |
| 189. #170 | #213 | semidirect |
| 267. C3×C5 | #1581 | semidirect |
| 314. C5 | #70862 | semidirect |
| 329. C3 | #10603940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65774 | 2 |
| #11751893 | 2 |
| #11748975 | 2 |
| D4⋊(C3⋊#170) | 2 |
| #11746514 | 2 |
| #11746490 | 2 |
| #170⋊(C3⋊C8) | 2 |
| #10603940 | 3 |
| #70862 | 5 |