Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
720 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 164 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. C2×C5×Dic24 | C2 | semidirect |
| 4. C2×C3×Dic40 | C2 | semidirect |
| 5. C2×#90946 | C2 | semidirect |
| 6. #11746831 | C2 | direct (N × H) |
| 18. C5×Dic24 | C22 | semidirect |
| 19. C3×Dic40 | C22 | semidirect |
| 20. #90946 | C22 | semidirect |
| 26. C2×Dic40 | D3 | semidirect |
| 50. C2×Dic24 | D5 | semidirect |
| 63. Dic40 | C2×D3 | semidirect |
| 93. Dic24 | C2×D5 | semidirect |
| 120. C2×D15 | Q32 | semidirect |
| 174. C2×C3×C5 | C2×Q32 | semidirect |
| 176. D15 | C2×Q32 | semidirect |
| 219. C3×C5 | C22×Q32 | semidirect |
| 228. C2×C5 | D3×Q32 | semidirect |
| 247. C2×C3 | D5×Q32 | semidirect |
| 250. C5 | C2×D3×Q32 | semidirect |
| 259. C3 | C2×D5×Q32 | semidirect |
| 261. C2 | #11746831 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91264 | 2 |
| C2×C16×D15 | 2 |
| C2×C5×Dic24 | 2 |
| C2×C3×Dic40 | 2 |
| C2×#90946 | 2 |
| #11746831 | 2 |
| C2×D5×Q32 | 3 |
| C2×D3×Q32 | 5 |