Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 96 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. C5×#5021 | C2 | semidirect |
| 3. #11747067 | C2 | semidirect |
| 4. #11746885 | C2 | semidirect |
| 5. C3×Q8⋊#168 | C2 | semidirect |
| 6. #11745854 | C2 | semidirect |
| 7. #11745839 | C2 | semidirect |
| 31. Q8⋊#168 | D3 | semidirect |
| 60. #5021 | D5 | semidirect |
| 87. C3×C5×Q8 | SD16 | semidirect |
| 205. C5×Q8 | #204 | semidirect |
| 253. C3×Q8 | #688 | semidirect |
| 318. C3×C5 | #1631 | semidirect |
| 344. Q8 | #6660 | semidirect |
| 372. C5 | #68261 | semidirect |
| 389. C3 | #10601953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756336 | 2 |
| C5×#5021 | 2 |
| #11747067 | 2 |
| #11746885 | 2 |
| C3×Q8⋊#168 | 2 |
| #11745854 | 2 |
| #11745839 | 2 |
| #10601953 | 3 |
| #68261 | 5 |