Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 103 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. C3×C5×C8×Q8 | C2 | semidirect |
| 3. #11751122 | C2 | semidirect |
| 6. #11746302 | C2 | semidirect |
| 7. #11746278 | C2 | semidirect |
| 25. C5×C8×Q8 | D3 | semidirect |
| 49. C3×C8×Q8 | D5 | semidirect |
| 127. C8×Q8 | D15 | semidirect |
| 248. C3×C5 | #1678 | semidirect |
| 289. C5 | #70940 | semidirect |
| 302. C3 | #10601733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C8×Q8 | 2 |
| #11751128 | 2 |
| #11751122 | 2 |
| #11750795 | 2 |
| #11746306 | 2 |
| #11746302 | 2 |
| #11746278 | 2 |
| #10601733 | 3 |
| #70940 | 5 |