Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 332 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 |
|---|---|---|
| 2. C3×#64969 | C2 | semidirect |
| 5. C5×#4457 | C2 | semidirect |
| 6. #11745861 | C2 | semidirect |
| 7. #11745856 | C2 | semidirect |
| 28. #64969 | D3 | semidirect |
| 56. #4457 | D5 | semidirect |
| 88. C3×C5×C8 | SD16 | semidirect |
| 179. C5×C8 | #215 | semidirect |
| 215. C3×C8 | #677 | semidirect |
| 249. C3×C5 | #1671 | semidirect |
| 284. C8 | #6658 | semidirect |
| 289. C5 | #71344 | semidirect |
| 302. C3 | #10599330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D60 | 2 |
| C3×#64969 | 2 |
| #11747085 | 2 |
| #11746942 | 2 |
| C5×#4457 | 2 |
| #11745861 | 2 |
| #11745856 | 2 |
| #10599330 | 3 |
| #71344 | 5 |