Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
556 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 556 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 |
|---|---|---|
| 1. #11756336 | C2 | semidirect |
| 2. C5×#5027 | C2 | semidirect |
| 3. #11747045 | C2 | semidirect |
| 4. #11747029 | C2 | semidirect |
| 5. C3×Q8⋊#168 | C2 | semidirect |
| 6. #11745854 | C2 | semidirect |
| 7. #11745839 | C2 | semidirect |
| 31. Q8⋊#168 | D3 | semidirect |
| 62. #5027 | D5 | semidirect |
| 90. C3×C5×Q8 | D8 | semidirect |
| 217. C5×Q8 | D24 | semidirect |
| 271. C3×Q8 | #686 | semidirect |
| 343. C3×C5 | #1621 | semidirect |
| 372. Q8 | #6654 | semidirect |
| 405. C5 | #68259 | 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 |
| C5×#5027 | 2 |
| #11747045 | 2 |
| #11747029 | 2 |
| C3×Q8⋊#168 | 2 |
| #11745854 | 2 |
| #11745839 | 2 |
| #10601825 | 3 |
| #68259 | 5 |