Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11751297 | C2 | semidirect |
| 3. #11750996 | C2 | semidirect |
| 4. C3×C5×#359 | C2 | semidirect |
| 5. #11746331 | C2 | semidirect |
| 6. #11746323 | C2 | semidirect |
| 7. #11746314 | C2 | semidirect |
| 16. #91113 | C4 | semidirect |
| 17. #91112 | C4 | semidirect |
| 18. #91111 | C4 | semidirect |
| 19. #91110 | C4 | semidirect |
| 28. C5×#359 | D3 | semidirect |
| 55. C3×#359 | D5 | semidirect |
| 131. #359 | D15 | semidirect |
| 240. C3×C5 | #2179 | semidirect |
| 273. C5 | #69239 | semidirect |
| 282. C3 | #10600032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751297 | 2 |
| #11751295 | 2 |
| #11750996 | 2 |
| C3×C5×#359 | 2 |
| #11746331 | 2 |
| #11746323 | 2 |
| #11746314 | 2 |
| #10600032 | 3 |
| #69239 | 5 |