Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C5×Dic3×Q16 | C2 | semidirect |
| 4. C3×#64784 | C2 | semidirect |
| 5. #11745943 | C2 | semidirect |
| 7. Dic3×#672 | C2 | semidirect |
| 13. #91112 | C4 | semidirect |
| 25. #64784 | D3 | semidirect |
| 33. C3×C5×Q16 | C2×C4 | semidirect |
| 44. C3⋊#672 | C2×C4 | semidirect |
| 46. Dic3×Q16 | D5 | semidirect |
| 97. C5×Q16 | C4×D3 | semidirect |
| 127. C5×Dic3 | SD32 | semidirect |
| 132. C3×Q16 | C4×D5 | semidirect |
| 206. Q16 | #1200 | semidirect |
| 219. C3×C5 | C4×SD32 | semidirect |
| 230. Dic3 | #3960 | semidirect |
| 254. C5 | #69206 | 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 |
|---|---|
| C2×#91112 | 2 |
| C5×Dic3×Q16 | 2 |
| #11747793 | 2 |
| C3×#64784 | 2 |
| #11745943 | 2 |
| #11745896 | 2 |
| Dic3×#672 | 2 |
| C4×#3960 | 3 |
| #69206 | 5 |