Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C3×C5×#368 | C2 | semidirect |
| 4. #11746327 | C2 | semidirect |
| 5. #11746314 | C2 | semidirect |
| 19. C5×#368 | D3 | semidirect |
| 37. C3×#368 | D5 | semidirect |
| 89. #368 | D15 | direct (N × H) |
| 136. D15 | #368 | direct (N × H) |
| 171. C3×C5 | C2×#368 | semidirect |
| 201. C5 | D3×#368 | semidirect |
| 210. C3 | D5×#368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D15 | 2 |
| D15×#108 | 2 |
| C3×C5×#368 | 2 |
| #11746327 | 2 |
| #11746314 | 2 |
| D5×#368 | 3 |
| D3×#368 | 5 |