Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 86 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. #11751189 | C2 | semidirect |
| 2. C5×#5083 | C2 | semidirect |
| 4. #11746998 | C2 | semidirect |
| 5. C3×#64767 | C2 | semidirect |
| 6. #11745868 | C2 | semidirect |
| 7. #11745854 | C2 | semidirect |
| 29. #64767 | D3 | semidirect |
| 52. #5083 | D5 | semidirect |
| 270. C3×C5 | #1681 | semidirect |
| 318. C5 | #68446 | semidirect |
| 333. C3 | #10601832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751189 | 2 |
| C5×#5083 | 2 |
| #11747037 | 2 |
| #11746998 | 2 |
| C3×#64767 | 2 |
| #11745868 | 2 |
| #11745854 | 2 |
| #10601832 | 3 |
| #68446 | 5 |