Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
468 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 92 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. C4×#6739 | C2 | semidirect |
| 3. D3×C4⋊#170 | C2 | semidirect |
| 4. D4⋊(C3⋊#170) | C2 | semidirect |
| 5. C3×D4⋊#170 | C2 | semidirect |
| 6. #11746495 | C2 | semidirect |
| 7. #11746494 | C2 | semidirect |
| 33. D4⋊#170 | D3 | semidirect |
| 346. C3×C5 | #1483 | semidirect |
| 402. C5 | #68170 | semidirect |
| 421. C3 | #10604479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11754848 | 2 |
| C4×#6739 | 2 |
| D3×C4⋊#170 | 2 |
| D4⋊(C3⋊#170) | 2 |
| C3×D4⋊#170 | 2 |
| #11746495 | 2 |
| #11746494 | 2 |
| #10604479 | 3 |
| #68170 | 5 |