Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 84 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. #11750942 | C2 | semidirect |
| 3. #11746994 | C2 | semidirect |
| 4. #11746890 | C2 | semidirect |
| 5. C5×#4479 | C2 | semidirect |
| 6. C3×#64705 | C2 | semidirect |
| 7. #11745859 | C2 | semidirect |
| 30. #64705 | D3 | semidirect |
| 57. #4479 | D5 | semidirect |
| 270. C3×C5 | #1681 | semidirect |
| 318. C5 | #68397 | semidirect |
| 333. C3 | #10599373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750942 | 2 |
| #11747043 | 2 |
| #11746994 | 2 |
| #11746890 | 2 |
| C5×#4479 | 2 |
| C3×#64705 | 2 |
| #11745859 | 2 |
| #10599373 | 3 |
| #68397 | 5 |