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 |
|---|---|---|
| 1. #11756314 | C2 | semidirect |
| 2. C5×#5015 | C2 | semidirect |
| 3. #11747045 | C2 | semidirect |
| 4. #11746906 | C2 | semidirect |
| 5. C3×D4⋊#168 | C2 | semidirect |
| 6. #11745859 | C2 | semidirect |
| 7. #11745839 | C2 | semidirect |
| 31. D4⋊#168 | D3 | semidirect |
| 61. #5015 | D5 | semidirect |
| 89. C3×C5×D4 | D8 | semidirect |
| 217. C5×D4 | D24 | semidirect |
| 264. C3×D4 | #686 | semidirect |
| 333. C3×C5 | #1625 | semidirect |
| 372. D4 | #6654 | semidirect |
| 393. C5 | #68200 | semidirect |
| 412. C3 | #10601811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756314 | 2 |
| C5×#5015 | 2 |
| #11747045 | 2 |
| #11746906 | 2 |
| C3×D4⋊#168 | 2 |
| #11745859 | 2 |
| #11745839 | 2 |
| #10601811 | 3 |
| #68200 | 5 |