Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
372 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×C3×C5×D16 | C2 | semidirect |
| 2. #11751252 | C2 | semidirect |
| 3. D8×Dic15 | C2 | semidirect |
| 4. C2×#91110 | C2 | semidirect |
| 5. #11746383 | C2 | semidirect |
| 6. #11746330 | C2 | semidirect |
| 7. #11746322 | C2 | semidirect |
| 23. C2×C5×D16 | D3 | semidirect |
| 39. C3×C5×D8 | D4 | semidirect |
| 50. C2×C3×D16 | D5 | semidirect |
| 112. C5×D8 | #67 | semidirect |
| 124. C2×D16 | D15 | semidirect |
| 144. Dic15 | D16 | semidirect |
| 154. C3×D8 | C22⋊D5 | semidirect |
| 249. D8 | #1220 | semidirect |
| 257. C3×C5 | #2206 | semidirect |
| 304. C5 | #71462 | semidirect |
| 320. C3 | #10602255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D16 | 2 |
| #11751252 | 2 |
| D8×Dic15 | 2 |
| C2×#91110 | 2 |
| #11746383 | 2 |
| #11746330 | 2 |
| #11746322 | 2 |
| #10602255 | 3 |
| #71462 | 5 |