Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 87 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×C3×C5×SD32 | C2 | semidirect |
| 3. #11751289 | C2 | semidirect |
| 4. C2×#91112 | C2 | semidirect |
| 5. #11746383 | C2 | semidirect |
| 6. #11746330 | C2 | semidirect |
| 7. #11746328 | C2 | semidirect |
| 10. C2×C3×C5×Q16 | C22 | semidirect |
| 19. C2×C3×C5×C16 | C22 | semidirect |
| 22. #91102 | C22 | semidirect |
| 23. C2×C3⋊#672 | C22 | semidirect |
| 26. C2×C5×SD32 | D3 | semidirect |
| 57. C2×C3×SD32 | D5 | semidirect |
| 64. C2×C5×Q16 | C2×D3 | semidirect |
| 73. C2×C5×C16 | C2×D3 | semidirect |
| 102. C2×C3×Q16 | C2×D5 | semidirect |
| 111. C2×C3×C16 | C2×D5 | semidirect |
| 142. C2×SD32 | D15 | semidirect |
| 157. C2×D15 | SD32 | semidirect |
| 210. C2×Q16 | C2×D15 | semidirect |
| 221. C2×C16 | C2×D15 | semidirect |
| 292. C3×C5 | #2187 | semidirect |
| 343. C5 | #71485 | semidirect |
| 360. C3 | #10602278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D15 | 2 |
| C2×C3×C5×SD32 | 2 |
| #11751289 | 2 |
| C2×#91112 | 2 |
| #11746383 | 2 |
| #11746330 | 2 |
| #11746328 | 2 |
| #10602278 | 3 |
| #71485 | 5 |