Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
368 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 3. #11746755 | C2 | semidirect |
| 4. C3×#64884 | C2 | semidirect |
| 5. #11746514 | C2 | semidirect |
| 22. #64884 | D3 | semidirect |
| 73. C3×#168 | M16 | semidirect |
| 74. C5×C3⋊C8 | M16 | semidirect |
| 152. #168 | ΓL(1,𝔽25) | semidirect |
| 185. C3⋊C8 | #704 | semidirect |
| 214. C3×C5 | #1567 | semidirect |
| 253. C5 | #68569 | semidirect |
| 266. C3 | #10604697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751921 | 2 |
| D3×C8×Dic5 | 2 |
| #11746755 | 2 |
| C3×#64884 | 2 |
| #11746514 | 2 |
| #10604697 | 3 |
| #68569 | 5 |