Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
336 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 86 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. #11746949 | C2 | semidirect |
| 4. #11746865 | C2 | semidirect |
| 5. C5×#4479 | C2 | semidirect |
| 6. C3×#64706 | C2 | semidirect |
| 30. #64706 | D3 | semidirect |
| 57. #4479 | D5 | semidirect |
| 94. C5×C3⋊C8 | SD16 | semidirect |
| 227. C3⋊C8 | #677 | semidirect |
| 259. C3×C5 | #1686 | semidirect |
| 301. C5 | #68472 | semidirect |
| 314. C3 | #10599385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750949 | 2 |
| #11747075 | 2 |
| #11746949 | 2 |
| #11746865 | 2 |
| C5×#4479 | 2 |
| C3×#64706 | 2 |
| #11745854 | 2 |
| #10599385 | 3 |
| #68472 | 5 |