Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
800 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 298 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. C22×C3×C5×Q16 | C2 | semidirect |
| 3. C2×C3×#3960 | C2 | direct (N × H) |
| 4. C22×C3×#672 | C2 | semidirect |
| 5. C22×#3960 | C3 | direct (N × H) |
| 9. C2×C3×C5×Q16 | C22 | semidirect |
| 13. C3×#3960 | C22 | direct (N × H) |
| 14. C2×C3×#672 | C22 | semidirect |
| 16. C22×C5×Q16 | C2×C3 | semidirect |
| 18. C2×#3960 | C2×C3 | direct (N × H) |
| 19. C22×#672 | C2×C3 | semidirect |
| 28. C3×C5×Q16 | C23 | semidirect |
| 33. C3×#672 | C23 | semidirect |
| 34. C22×C3×Q16 | D5 | semidirect |
| 41. C2×C5×Q16 | C22×C3 | semidirect |
| 45. #3960 | C22×C3 | direct (N × H) |
| 46. C2×#672 | C22×C3 | semidirect |
| 63. C2×C3×Q16 | C2×D5 | semidirect |
| 77. C5×Q16 | C23×C3 | semidirect |
| 82. #672 | C23×C3 | semidirect |
| 83. C22×Q16 | C3×D5 | semidirect |
| 87. C22×C3×C5 | SD32 | semidirect |
| 102. C3×Q16 | C22×D5 | semidirect |
| 123. C2×Q16 | C2×C3×D5 | semidirect |
| 129. C2×C3×C5 | C2×SD32 | semidirect |
| 144. C22×C5 | C3×SD32 | semidirect |
| 159. Q16 | C22×C3×D5 | semidirect |
| 165. C3×C5 | C22×SD32 | semidirect |
| 168. C22×C3 | #3960 | direct (N × H) |
| 173. C2×C5 | C2×C3×SD32 | semidirect |
| 189. C2×C3 | C2×#3960 | direct (N × H) |
| 191. C5 | C22×C3×SD32 | semidirect |
| 194. C22 | C3×#3960 | direct (N × H) |
| 199. C3 | C22×#3960 | direct (N × H) |
| 201. C2 | C2×C3×#3960 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×Q16 | 2 |
| C22×C3×D40 | 2 |
| C2×C3×#3960 | 2 |
| C22×C3×#672 | 2 |
| C22×#3960 | 3 |
| C22×C3×SD32 | 5 |