Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
496 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 110 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. #11746801 | C2 | semidirect |
| 5. C3×Q8⋊#170 | C2 | semidirect |
| 6. #11746495 | C2 | semidirect |
| 7. #11746494 | C2 | semidirect |
| 33. Q8⋊#170 | D3 | semidirect |
| 38. Q8×D15 | C8 | semidirect |
| 341. C3×C5 | #1479 | semidirect |
| 393. C5 | #68231 | semidirect |
| 410. C3 | #10604438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#1200 | 2 |
| #11751812 | 2 |
| #11751777 | 2 |
| #11746801 | 2 |
| C3×Q8⋊#170 | 2 |
| #11746495 | 2 |
| #11746494 | 2 |
| #10604438 | 3 |
| #68231 | 5 |