Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
736 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 167 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×#91801 | C2 | semidirect |
| 2. C2×C3×C5×D16 | C2 | semidirect |
| 3. C2×#91111 | C2 | semidirect |
| 4. #11751013 | C2 | direct (N × H) |
| 5. C2×Dic120 | C2 | semidirect |
| 6. C2×C16×D15 | C2 | semidirect |
| 12. #91801 | C22 | semidirect |
| 15. C3×C5×D16 | C22 | semidirect |
| 17. #91111 | C22 | semidirect |
| 19. Dic120 | C22 | semidirect |
| 20. C16×D15 | C22 | semidirect |
| 23. C2×C5×D16 | D3 | semidirect |
| 47. C2×C3×D16 | D5 | semidirect |
| 59. C5×D16 | C2×D3 | semidirect |
| 89. C3×D16 | C2×D5 | semidirect |
| 117. C2×D16 | D15 | semidirect |
| 171. D16 | C2×D15 | semidirect |
| 176. C2×C3×C5 | #508 | semidirect |
| 222. C3×C5 | C2×#508 | semidirect |
| 233. C2×C5 | #4912 | semidirect |
| 253. C2×C3 | #65201 | semidirect |
| 256. C5 | C2×#4912 | semidirect |
| 266. C3 | C2×#65201 | semidirect |
| 269. C2 | #11751013 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91801 | 2 |
| C2×C3×C5×D16 | 2 |
| C2×#91111 | 2 |
| #11751013 | 2 |
| C2×Dic120 | 2 |
| C2×C16×D15 | 2 |
| C2×#65201 | 3 |
| C2×#4912 | 5 |