Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
556 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #11756336 | C2 | semidirect |
| 2. C3×C5×#460 | C2 | semidirect |
| 3. #11751174 | C2 | semidirect |
| 4. #11751173 | C2 | semidirect |
| 5. #11746356 | C2 | semidirect |
| 6. #11746306 | C2 | semidirect |
| 7. #11746304 | C2 | semidirect |
| 28. C5×#460 | D3 | semidirect |
| 62. C3×#460 | D5 | semidirect |
| 90. C3×C5×Q8 | D8 | semidirect |
| 163. #460 | D15 | semidirect |
| 217. C5×Q8 | #213 | semidirect |
| 271. C3×Q8 | #686 | semidirect |
| 343. C3×C5 | #1621 | semidirect |
| 372. Q8 | #6715 | semidirect |
| 405. C5 | #71032 | semidirect |
| 424. C3 | #10601825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756336 | 2 |
| C3×C5×#460 | 2 |
| #11751174 | 2 |
| #11751173 | 2 |
| #11746356 | 2 |
| #11746306 | 2 |
| #11746304 | 2 |
| #10601825 | 3 |
| #71032 | 5 |