Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 348 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. C2×#90933 | C2 | semidirect |
| 3. C4×C5×C3⋊C16 | C2 | semidirect |
| 4. C3×C4⋊#672 | C2 | semidirect |
| 5. #11745881 | C2 | semidirect |
| 21. C4⋊#672 | D3 | semidirect |
| 34. C5×C3⋊C16 | D4 | semidirect |
| 39. C4×C3⋊C16 | D5 | semidirect |
| 55. D60 | C16 | semidirect |
| 92. C2×D15 | C2×C16 | semidirect |
| 94. C3×C4×C5 | C2×C16 | semidirect |
| 110. C3⋊C16 | D20 | semidirect |
| 153. C4×C5 | D3×C16 | semidirect |
| 170. C3×C5 | D4×C16 | semidirect |
| 176. C3×C4 | D5×C16 | semidirect |
| 200. C5 | #69277 | semidirect |
| 207. C4 | #90933 | semidirect |
| 210. C3 | C16×D20 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D60 | 2 |
| C2×#90933 | 2 |
| C4×C5×C3⋊C16 | 2 |
| C3×C4⋊#672 | 2 |
| #11745881 | 2 |
| C16×D20 | 3 |
| #69277 | 5 |