Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
396 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 116 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. #11750783 | C2 | semidirect |
| 4. #11746941 | C2 | semidirect |
| 5. #11746930 | C2 | semidirect |
| 7. C3×#64675 | C2 | semidirect |
| 29. #64675 | D3 | semidirect |
| 82. C3×C5×C8 | SD16 | semidirect |
| 164. C5×C8 | #204 | semidirect |
| 199. C3×C8 | #687 | semidirect |
| 228. C3×C5 | #1714 | semidirect |
| 258. C8 | #6659 | semidirect |
| 263. C5 | #68090 | semidirect |
| 274. C3 | #10602051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750783 | 2 |
| C5×#4693 | 2 |
| #11747066 | 2 |
| #11746941 | 2 |
| #11746930 | 2 |
| #11746906 | 2 |
| C3×#64675 | 2 |
| #10602051 | 3 |
| #68090 | 5 |