Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 74 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. #11753963 | C2 | semidirect |
| 2. C3×#65186 | C2 | semidirect |
| 3. C2×#90938 | C2 | semidirect |
| 4. #11747539 | C2 | semidirect |
| 5. #11746316 | C2 | semidirect |
| 6. C5×#4497 | C2 | semidirect |
| 7. #11745886 | C2 | semidirect |
| 13. C2×C3×D40 | C22 | semidirect |
| 19. C3×C5×#108 | C22 | semidirect |
| 20. #91096 | C22 | semidirect |
| 21. C2×C5×C3⋊C16 | C22 | semidirect |
| 30. #65186 | D3 | semidirect |
| 66. #4497 | D5 | semidirect |
| 76. C2×D40 | C2×D3 | semidirect |
| 79. C5×#108 | C2×D3 | semidirect |
| 119. C3×#108 | C2×D5 | semidirect |
| 125. C2×C3⋊C16 | C2×D5 | semidirect |
| 237. #108 | D3×D5 | semidirect |
| 307. C3×C5 | #2192 | semidirect |
| 355. C5 | #71094 | semidirect |
| 368. C3 | #10600035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11753963 | 2 |
| C3×#65186 | 2 |
| C2×#90938 | 2 |
| #11747539 | 2 |
| #11746316 | 2 |
| C5×#4497 | 2 |
| #11745886 | 2 |
| #10600035 | 3 |
| #71094 | 5 |