Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 94 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. #11751789 | C2 | semidirect |
| 4. #11746752 | C2 | semidirect |
| 5. C3×C8×#170 | C2 | semidirect |
| 6. #11746493 | C2 | semidirect |
| 31. C8×#170 | D3 | semidirect |
| 90. C3×#170 | SD16 | semidirect |
| 91. C3×C5×C8 | M16 | semidirect |
| 180. #170 | #204 | semidirect |
| 181. C5×C8 | ΓL(1,𝔽25) | semidirect |
| 219. C3×C8 | #704 | semidirect |
| 252. C3×C5 | #1590 | semidirect |
| 288. C8 | #6739 | semidirect |
| 293. C5 | #68055 | semidirect |
| 306. C3 | #10604813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751913 | 2 |
| #11751789 | 2 |
| Dic5×#204 | 2 |
| #11746752 | 2 |
| C3×C8×#170 | 2 |
| #11746493 | 2 |
| #11746489 | 2 |
| #10604813 | 3 |
| #68055 | 5 |