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. #11746493 | C2 | semidirect |
| 7. #11746492 | C2 | semidirect |
| 35. Q8⋊#170 | D3 | semidirect |
| 95. C3×C5×Q8 | M16 | semidirect |
| 108. C5×Dic6 | M16 | semidirect |
| 227. C5×Q8 | ΓL(1,𝔽25) | semidirect |
| 274. C3×Q8 | #704 | semidirect |
| 294. Dic6 | #704 | semidirect |
| 345. C3×C5 | #1487 | semidirect |
| 371. Q8 | #6739 | semidirect |
| 397. C5 | #68236 | semidirect |
| 414. C3 | #10604968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Q8×Dic5 | 2 |
| #11751921 | 2 |
| #11751795 | 2 |
| #11746801 | 2 |
| C3×Q8⋊#170 | 2 |
| #11746493 | 2 |
| #11746492 | 2 |
| #10604968 | 3 |
| #68236 | 5 |