Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 98 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. D8×Dic15 | C2 | semidirect |
| 3. #11747809 | C2 | semidirect |
| 4. C5×#4562 | C2 | semidirect |
| 5. #11745939 | C2 | semidirect |
| 6. #11745892 | C2 | semidirect |
| 7. #11745872 | C2 | semidirect |
| 18. C3×#3958 | C4 | semidirect |
| 34. C3×C5×D8 | C2×C4 | semidirect |
| 42. C3×D40 | C2×C4 | semidirect |
| 44. C3×#672 | C2×C4 | semidirect |
| 50. #4562 | D5 | semidirect |
| 60. #3958 | Dic3 | semidirect |
| 99. C5×D8 | C2×Dic3 | semidirect |
| 108. D40 | C2×Dic3 | semidirect |
| 110. #672 | C2×Dic3 | semidirect |
| 129. Dic15 | D16 | semidirect |
| 138. C3×D8 | C4×D5 | semidirect |
| 217. D8 | D5×Dic3 | semidirect |
| 227. C3×C5 | C4×D16 | semidirect |
| 267. C5 | Dic3×D16 | semidirect |
| 281. C3 | #10599967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic15 | 2 |
| C2×C3×#3958 | 2 |
| #11747809 | 2 |
| C5×#4562 | 2 |
| #11745939 | 2 |
| #11745892 | 2 |
| #11745872 | 2 |
| #10599967 | 3 |
| Dic3×D16 | 5 |