Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. Q16×Dic15 | C2 | semidirect |
| 4. #11746385 | C2 | semidirect |
| 6. #11746326 | C2 | semidirect |
| 7. C16×Dic15 | C2 | semidirect |
| 13. C3×C5×SD32 | C4 | semidirect |
| 33. C3×C5×Q16 | C2×C4 | semidirect |
| 44. C3×C5×C16 | C2×C4 | semidirect |
| 57. C5×SD32 | Dic3 | semidirect |
| 85. C3×SD32 | Dic5 | semidirect |
| 97. C5×Q16 | C2×Dic3 | semidirect |
| 108. C5×C16 | C2×Dic3 | semidirect |
| 127. Dic15 | SD32 | direct (N × H) |
| 132. C3×Q16 | C2×Dic5 | semidirect |
| 143. C3×C16 | C2×Dic5 | semidirect |
| 164. SD32 | Dic15 | direct (N × H) |
| 206. Q16 | C2×Dic15 | semidirect |
| 218. C16 | C2×Dic15 | semidirect |
| 219. C3×C5 | C4×SD32 | semidirect |
| 254. C5 | Dic3×SD32 | semidirect |
| 266. C3 | Dic5×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×SD32 | 2 |
| Q16×Dic15 | 2 |
| D8×Dic15 | 2 |
| #11746385 | 2 |
| #11746383 | 2 |
| #11746326 | 2 |
| C16×Dic15 | 2 |
| Dic5×SD32 | 3 |
| Dic3×SD32 | 5 |