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. #11751122 | C2 | semidirect |
| 2. C5×Q8×C3⋊C8 | C2 | semidirect |
| 5. #11745866 | C2 | semidirect |
| 6. #11745863 | C2 | semidirect |
| 51. Q8×C3⋊C8 | D5 | semidirect |
| 248. C3×C5 | #1678 | semidirect |
| 289. C5 | #71022 | semidirect |
| 302. C3 | #10601733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751122 | 2 |
| C5×Q8×C3⋊C8 | 2 |
| C3×#65316 | 2 |
| #11746890 | 2 |
| #11745866 | 2 |
| #11745863 | 2 |
| #11745852 | 2 |
| #10601733 | 3 |
| #71022 | 5 |