Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
648 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 106 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. #11756989 | C2 | semidirect |
| 3. C3×#65784 | C2 | semidirect |
| 4. D5⋊#823 | C2 | semidirect |
| 5. #11751706 | C2 | semidirect |
| 6. #11746537 | C2 | semidirect |
| 7. #11746521 | C2 | semidirect |
| 18. C2×#6717 | C4 | semidirect |
| 19. C2×C5×#215 | C4 | semidirect |
| 22. C2×#6653 | C4 | semidirect |
| 23. C2×#6652 | C4 | semidirect |
| 31. #65784 | D3 | semidirect |
| 145. C2×#215 | AGL(1,𝔽5) | semidirect |
| 409. C3×C5 | #1903 | semidirect |
| 476. C5 | #70400 | semidirect |
| 495. C3 | #10604827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756989 | 2 |
| C2×#91502 | 2 |
| C3×#65784 | 2 |
| D5⋊#823 | 2 |
| #11751706 | 2 |
| #11746537 | 2 |
| #11746521 | 2 |
| #10604827 | 3 |
| #70400 | 5 |