Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 86 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. #11751826 | C2 | semidirect |
| 4. C8×C3⋊#170 | C2 | semidirect |
| 5. C3×#64883 | C2 | semidirect |
| 6. #11746494 | C2 | semidirect |
| 29. #64883 | D3 | semidirect |
| 88. C3⋊#170 | SD16 | semidirect |
| 92. C3×#168 | M16 | semidirect |
| 182. #168 | ΓL(1,𝔽25) | semidirect |
| 252. C3×C5 | #1590 | semidirect |
| 293. C5 | #68523 | semidirect |
| 306. C3 | #10603948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751927 | 2 |
| #11751826 | 2 |
| #11747744 | 2 |
| C8×C3⋊#170 | 2 |
| C3×#64883 | 2 |
| #11746494 | 2 |
| #11746488 | 2 |
| #10603948 | 3 |
| #68523 | 5 |