Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 102 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. #11751921 | C2 | semidirect |
| 3. C4×#6739 | C2 | semidirect |
| 4. #11746801 | C2 | semidirect |
| 5. C3×Q8⋊#170 | C2 | semidirect |
| 6. #11746489 | C2 | semidirect |
| 7. #11746488 | C2 | semidirect |
| 33. Q8⋊#170 | D3 | semidirect |
| 97. C3×C5×Q8 | M16 | semidirect |
| 106. C5×D12 | M16 | semidirect |
| 232. C5×Q8 | ΓL(1,𝔽25) | semidirect |
| 285. C3×Q8 | #704 | semidirect |
| 297. D12 | #704 | semidirect |
| 360. C3×C5 | #1489 | semidirect |
| 387. Q8 | #6739 | semidirect |
| 418. C5 | #68238 | semidirect |
| 437. C3 | #10605003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic5×#239 | 2 |
| #11751921 | 2 |
| C4×#6739 | 2 |
| #11746801 | 2 |
| C3×Q8⋊#170 | 2 |
| #11746489 | 2 |
| #11746488 | 2 |
| #10605003 | 3 |
| #68238 | 5 |