Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
428 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 3. #11746750 | C2 | semidirect |
| 4. C3×C8×#170 | C2 | semidirect |
| 5. #170⋊(C3⋊C8) | C2 | semidirect |
| 23. C8×#170 | D3 | semidirect |
| 64. C3×#170 | M16 | semidirect |
| 65. C3×C5×C8 | M16 | semidirect |
| 67. C3×#168 | M16 | semidirect |
| 130. #170 | ΓL(1,𝔽25) | semidirect |
| 132. C5×C8 | ΓL(1,𝔽25) | semidirect |
| 134. #168 | ΓL(1,𝔽25) | semidirect |
| 159. C3×C8 | #700 | semidirect |
| 185. C3×C5 | #1455 | semidirect |
| 210. C8 | #6740 | semidirect |
| 214. C5 | #68050 | semidirect |
| 223. C3 | #10603864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6740 | 2 |
| #11747592 | 2 |
| #11746750 | 2 |
| C3×C8×#170 | 2 |
| #170⋊(C3⋊C8) | 2 |
| #10603864 | 3 |
| #68050 | 5 |