Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
376 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 96 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. C8×D60 | C2 | semidirect |
| 2. C5×#4693 | C2 | semidirect |
| 4. #11746966 | C2 | semidirect |
| 5. C3×#64677 | C2 | semidirect |
| 6. #11745857 | C2 | semidirect |
| 7. #11745853 | C2 | semidirect |
| 31. #64677 | D3 | semidirect |
| 54. #4693 | D5 | semidirect |
| 82. D60 | SD16 | semidirect |
| 94. C3×C5×C8 | D8 | semidirect |
| 193. C5×C8 | D24 | semidirect |
| 238. C3×C8 | #686 | semidirect |
| 274. C3×C5 | #1665 | semidirect |
| 316. C8 | #6654 | semidirect |
| 322. C5 | #68536 | semidirect |
| 337. C3 | #10602060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D60 | 2 |
| C5×#4693 | 2 |
| #11747045 | 2 |
| #11746966 | 2 |
| C3×#64677 | 2 |
| #11745857 | 2 |
| #11745853 | 2 |
| #10602060 | 3 |
| #68536 | 5 |