Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
284 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 75 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. #11752398 | C2 | semidirect |
| 4. #11746781 | C2 | semidirect |
| 6. #11746719 | C2 | semidirect |
| 7. #11746716 | C2 | semidirect |
| 19. C3×C5×Q32 | C4 | semidirect |
| 20. C3×#3961 | C4 | semidirect |
| 21. C3×#3960 | C4 | semidirect |
| 22. C3×#3932 | C4 | semidirect |
| 69. C5×Q32 | Dic3 | semidirect |
| 70. #3961 | Dic3 | semidirect |
| 71. #3960 | Dic3 | semidirect |
| 72. #3932 | Dic3 | semidirect |
| 95. C3×Q32 | AGL(1,𝔽5) | semidirect |
| 181. Q32 | ΓL(1,𝔽16) | semidirect |
| 238. C3×C5 | #2180 | semidirect |
| 269. C5 | #71521 | semidirect |
| 279. C3 | #10604139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752400 | 2 |
| #11752398 | 2 |
| C3×#65207 | 2 |
| #11746781 | 2 |
| #11746778 | 2 |
| #11746719 | 2 |
| #11746716 | 2 |
| #10604139 | 3 |
| #71521 | 5 |