Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#91113 | C2 | semidirect |
| 4. #11746385 | C2 | semidirect |
| 111. C22×C3×C5 | Q32 | semidirect |
| 186. C22×C5 | #829 | semidirect |
| 212. C3×C5 | #2188 | semidirect |
| 215. C22×C3 | #3961 | semidirect |
| 247. C5 | #72064 | semidirect |
| 250. C22 | #91113 | semidirect |
| 258. C3 | #10602857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×Q16 | 2 |
| C2×#91113 | 2 |
| #11751217 | 2 |
| #11746385 | 2 |
| #11746370 | 2 |
| #10602857 | 3 |
| #72064 | 5 |