Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11750973 | C2 | semidirect |
| 2. #11747809 | C2 | semidirect |
| 4. C5×#4489 | C2 | semidirect |
| 5. C3×#64711 | C2 | semidirect |
| 6. #11745896 | C2 | semidirect |
| 7. #11745872 | C2 | semidirect |
| 20. #90938 | C4 | semidirect |
| 28. #64711 | D3 | semidirect |
| 39. D120 | C2×C4 | semidirect |
| 42. C3×D40 | C2×C4 | semidirect |
| 45. C5×C3⋊C16 | C2×C4 | semidirect |
| 52. #4489 | D5 | semidirect |
| 108. D40 | C4×D3 | semidirect |
| 129. Dic15 | D16 | semidirect |
| 147. C3⋊C16 | C4×D5 | semidirect |
| 227. C3×C5 | C4×D16 | semidirect |
| 267. C5 | #69174 | semidirect |
| 281. C3 | #10600110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750973 | 2 |
| #11747809 | 2 |
| C2×#90938 | 2 |
| C5×#4489 | 2 |
| C3×#64711 | 2 |
| #11745896 | 2 |
| #11745872 | 2 |
| #10600110 | 3 |
| #69174 | 5 |