Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 99 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. #11751217 | C2 | semidirect |
| 3. C2×#91084 | C2 | semidirect |
| 4. C3×C5×C22⋊C16 | C2 | semidirect |
| 5. #11746330 | C2 | semidirect |
| 10. C2×Dic60 | C22 | semidirect |
| 14. C2×C3×C5×C16 | C22 | semidirect |
| 15. #91102 | C22 | semidirect |
| 22. C5×C22⋊C16 | D3 | semidirect |
| 45. C3×C22⋊C16 | D5 | semidirect |
| 54. C2×C5×C16 | C2×D3 | semidirect |
| 84. C2×C3×C16 | C2×D5 | semidirect |
| 110. C22⋊C16 | D15 | semidirect |
| 113. C22×C3×C5 | SD32 | semidirect |
| 168. C2×C16 | C2×D15 | semidirect |
| 196. C22×C5 | #800 | semidirect |
| 225. C3×C5 | #2187 | semidirect |
| 228. C22×C3 | #3932 | semidirect |
| 267. C5 | #69110 | semidirect |
| 274. C22 | #91084 | semidirect |
| 281. C3 | #10599903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D120 | 2 |
| #11751217 | 2 |
| C2×#91084 | 2 |
| C3×C5×C22⋊C16 | 2 |
| #11746330 | 2 |
| #10599903 | 3 |
| #69110 | 5 |