Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 104 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. C5×Dic3×Q16 | C2 | semidirect |
| 4. #11746385 | C2 | semidirect |
| 5. #11745942 | C2 | semidirect |
| 7. Dic3×#672 | C2 | semidirect |
| 18. C3×#3960 | C4 | semidirect |
| 33. C3×C5×Q16 | C2×C4 | semidirect |
| 45. C3×#672 | C2×C4 | semidirect |
| 47. Dic3×Q16 | D5 | semidirect |
| 60. #3960 | Dic3 | direct (N × H) |
| 97. C5×Q16 | C2×Dic3 | semidirect |
| 109. #672 | C2×Dic3 | semidirect |
| 127. C5×Dic3 | SD32 | semidirect |
| 132. C3×Q16 | C4×D5 | semidirect |
| 206. Q16 | D5×Dic3 | semidirect |
| 219. C3×C5 | C4×SD32 | semidirect |
| 230. Dic3 | #3960 | direct (N × H) |
| 254. C5 | Dic3×SD32 | semidirect |
| 266. C3 | C4×#3960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Dic3×Q16 | 2 |
| C2×C3×#3960 | 2 |
| Dic3×D40 | 2 |
| #11746385 | 2 |
| #11745942 | 2 |
| #11745891 | 2 |
| Dic3×#672 | 2 |
| C4×#3960 | 3 |
| Dic3×SD32 | 5 |