Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 4. #11746960 | C2 | semidirect |
| 5. #11746307 | C2 | semidirect |
| 6. C3×#64706 | C2 | semidirect |
| 7. #11745866 | C2 | semidirect |
| 30. #64706 | D3 | semidirect |
| 93. C5×C3⋊C8 | SD16 | semidirect |
| 224. C3⋊C8 | #687 | semidirect |
| 256. C3×C5 | #1693 | semidirect |
| 297. C5 | #68451 | semidirect |
| 310. C3 | #10601666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4838 | 2 |
| #11747077 | 2 |
| #11747070 | 2 |
| #11746960 | 2 |
| #11746307 | 2 |
| C3×#64706 | 2 |
| #11745866 | 2 |
| #10601666 | 3 |
| #68451 | 5 |