Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
376 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 376 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. #11751176 | C2 | semidirect |
| 3. C8×Dic30 | C2 | semidirect |
| 4. #11746365 | C2 | semidirect |
| 5. #11746279 | C2 | semidirect |
| 68. Dic30 | D8 | semidirect |
| 70. C3×C5×C8 | SD16 | semidirect |
| 144. C5×C8 | #214 | semidirect |
| 176. C3×C8 | #687 | semidirect |
| 205. C3×C5 | #1668 | semidirect |
| 237. C8 | #6716 | semidirect |
| 242. C5 | #71286 | semidirect |
| 254. C3 | #10602079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#493 | 2 |
| #11751176 | 2 |
| C8×Dic30 | 2 |
| #11746365 | 2 |
| #11746279 | 2 |
| #10602079 | 3 |
| #71286 | 5 |