Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
396 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 2. C3×#64970 | C2 | semidirect |
| 4. #11746960 | C2 | semidirect |
| 5. #11746948 | C2 | semidirect |
| 7. C5×#4454 | C2 | semidirect |
| 27. #64970 | D3 | semidirect |
| 54. #4454 | D5 | semidirect |
| 84. C5×C3⋊C8 | SD16 | semidirect |
| 199. C3⋊C8 | #677 | semidirect |
| 228. C3×C5 | #1714 | semidirect |
| 263. C5 | #71216 | semidirect |
| 274. C3 | #10598883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750794 | 2 |
| C3×#64970 | 2 |
| #11747075 | 2 |
| #11746960 | 2 |
| #11746948 | 2 |
| #11746910 | 2 |
| C5×#4454 | 2 |
| #10598883 | 3 |
| #71216 | 5 |