Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
300 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 13. C3×C5×Q32 | C4 | semidirect |
| 14. C3×#3961 | C4 | semidirect |
| 15. C3×Dic40 | C4 | semidirect |
| 47. C5×Q32 | Dic3 | semidirect |
| 48. #3961 | Dic3 | semidirect |
| 49. Dic40 | Dic3 | semidirect |
| 67. C3×Q32 | AGL(1,𝔽5) | semidirect |
| 94. ΓL(1,𝔽16) | Q32 | direct (N × H) |
| 127. Q32 | ΓL(1,𝔽16) | direct (N × H) |
| 168. C3×C5 | C4×Q32 | semidirect |
| 194. C5 | Dic3×Q32 | semidirect |
| 203. C3 | AGL(1,𝔽5)×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×ΓL(1,𝔽16) | 2 |
| C3×D5×Q32 | 2 |
| #11746779 | 2 |
| #11746720 | 2 |
| C16×ΓL(1,𝔽16) | 2 |
| AGL(1,𝔽5)×Q32 | 3 |
| Dic3×Q32 | 5 |