Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 320 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. #11750781 | C2 | semidirect |
| 5. C5×#4458 | C2 | semidirect |
| 6. #11745863 | C2 | semidirect |
| 7. #11745859 | C2 | semidirect |
| 56. #4458 | D5 | semidirect |
| 88. C3×C5×C8 | SD16 | semidirect |
| 179. C5×C8 | #214 | semidirect |
| 216. C3×C8 | #677 | semidirect |
| 249. C3×C5 | #1691 | semidirect |
| 284. C8 | #6657 | semidirect |
| 289. C5 | #70872 | semidirect |
| 302. C3 | #10599376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750781 | 2 |
| C3×#64977 | 2 |
| #11747062 | 2 |
| #11746881 | 2 |
| C5×#4458 | 2 |
| #11745863 | 2 |
| #11745859 | 2 |
| #10599376 | 3 |
| #70872 | 5 |