Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 440 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. C3×#66086 | C2 | semidirect |
| 2. C5×#5142 | C2 | semidirect |
| 3. #11747540 | C2 | semidirect |
| 4. C2×#90937 | C2 | semidirect |
| 5. #11746382 | C2 | semidirect |
| 6. #11745915 | C2 | semidirect |
| 7. #11745903 | C2 | semidirect |
| 12. C2×C5×D24 | C22 | semidirect |
| 19. #91096 | C22 | semidirect |
| 20. C2×C3⋊#672 | C22 | semidirect |
| 22. C5×#819 | C22 | semidirect |
| 27. #66086 | D3 | semidirect |
| 64. #5142 | D5 | semidirect |
| 118. C2×D24 | C2×D5 | semidirect |
| 123. #819 | C2×D5 | semidirect |
| 307. C3×C5 | #2192 | semidirect |
| 355. C5 | #72122 | semidirect |
| 368. C3 | #10601887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66086 | 2 |
| C5×#5142 | 2 |
| #11747540 | 2 |
| C2×#90937 | 2 |
| #11746382 | 2 |
| #11745915 | 2 |
| #11745903 | 2 |
| #10601887 | 3 |
| #72122 | 5 |