Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 332 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 |
| 2. #11751132 | C2 | semidirect |
| 5. #11746307 | C2 | semidirect |
| 7. #11746279 | C2 | semidirect |
| 25. C5×C8×Q8 | D3 | semidirect |
| 50. C3×C8×Q8 | D5 | semidirect |
| 130. C8×Q8 | D15 | semidirect |
| 255. C3×C5 | #1682 | semidirect |
| 297. C5 | #70941 | semidirect |
| 310. C3 | #10601734 | 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 |
| #11751132 | 2 |
| #11751128 | 2 |
| #11750795 | 2 |
| #11746307 | 2 |
| #11746306 | 2 |
| #11746279 | 2 |
| #10601734 | 3 |
| #70941 | 5 |