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. #11747810 | C2 | semidirect |
| 2. #11747809 | C2 | semidirect |
| 4. C16×Dic15 | C2 | semidirect |
| 5. C5×#4509 | C2 | semidirect |
| 6. C3×#64729 | C2 | semidirect |
| 7. #11745940 | C2 | semidirect |
| 20. #90937 | C4 | semidirect |
| 26. #64729 | D3 | semidirect |
| 38. C5×D24 | C2×C4 | semidirect |
| 41. C3×D40 | C2×C4 | semidirect |
| 45. C3⋊#672 | C2×C4 | semidirect |
| 50. #4509 | D5 | semidirect |
| 108. D40 | C4×D3 | semidirect |
| 128. Dic15 | D16 | semidirect |
| 145. D24 | C4×D5 | semidirect |
| 227. C3×C5 | C4×D16 | semidirect |
| 267. C5 | #69174 | semidirect |
| 281. C3 | #10599967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11747810 | 2 |
| #11747809 | 2 |
| C2×#90937 | 2 |
| C16×Dic15 | 2 |
| C5×#4509 | 2 |
| C3×#64729 | 2 |
| #11745940 | 2 |
| #10599967 | 3 |
| #69174 | 5 |