Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
664 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 100 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. #11750936 | C2 | semidirect |
| 3. #11746867 | C2 | semidirect |
| 4. C5×#4485 | C2 | semidirect |
| 5. C3×#64705 | C2 | semidirect |
| 6. #11745853 | C2 | semidirect |
| 7. #11745852 | C2 | semidirect |
| 18. C3×C5×C4⋊C8 | C22 | semidirect |
| 21. C4⋊(C3⋊#168) | C22 | semidirect |
| 22. C5×C4⋊(C3⋊C8) | C22 | semidirect |
| 23. C3×C4⋊#168 | C22 | semidirect |
| 33. #64705 | D3 | semidirect |
| 66. #4485 | D5 | semidirect |
| 77. C5×C4⋊C8 | C2×D3 | semidirect |
| 83. C4⋊#168 | C2×D3 | semidirect |
| 129. C3×C4⋊C8 | C2×D5 | semidirect |
| 135. C4⋊(C3⋊C8) | C2×D5 | semidirect |
| 260. C4⋊C8 | D3×D5 | semidirect |
| 350. C3×C5 | #1555 | semidirect |
| 416. C5 | #68387 | semidirect |
| 436. C3 | #10599180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752750 | 2 |
| #11750936 | 2 |
| #11746867 | 2 |
| C5×#4485 | 2 |
| C3×#64705 | 2 |
| #11745853 | 2 |
| #11745852 | 2 |
| #10599180 | 3 |
| #68387 | 5 |