Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
480 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 100 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×#65296 | C2 | semidirect |
| 3. #11747070 | C2 | semidirect |
| 4. #11746947 | C2 | semidirect |
| 5. D4⋊(C3⋊#168) | C2 | semidirect |
| 6. #11745858 | C2 | semidirect |
| 7. #11745836 | C2 | semidirect |
| 30. #65296 | D3 | semidirect |
| 87. C3×C5×D4 | SD16 | semidirect |
| 208. C5×D4 | #215 | semidirect |
| 253. C3×D4 | #687 | semidirect |
| 315. C3×C5 | #1654 | semidirect |
| 347. D4 | #6656 | semidirect |
| 368. C5 | #71111 | semidirect |
| 385. C3 | #10602706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5555 | 2 |
| C3×#65296 | 2 |
| #11747070 | 2 |
| #11746947 | 2 |
| D4⋊(C3⋊#168) | 2 |
| #11745858 | 2 |
| #11745836 | 2 |
| #10602706 | 3 |
| #71111 | 5 |