Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
368 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 108 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. #11746754 | C2 | semidirect |
| 4. C3×#64883 | C2 | semidirect |
| 5. #11746513 | C2 | semidirect |
| 23. #64883 | D3 | semidirect |
| 71. C3⋊#168 | M16 | semidirect |
| 72. C3×#168 | M16 | semidirect |
| 149. #168 | ΓL(1,𝔽25) | semidirect |
| 209. C3×C5 | #1566 | semidirect |
| 246. C5 | #68529 | semidirect |
| 258. C3 | #10603817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751922 | 2 |
| C8×#1200 | 2 |
| #11746754 | 2 |
| C3×#64883 | 2 |
| #11746513 | 2 |
| #10603817 | 3 |
| #68529 | 5 |