Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
624 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 106 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. #11751922 | C2 | semidirect |
| 3. #11751797 | C2 | semidirect |
| 4. #11746742 | C2 | semidirect |
| 5. C3×#64871 | C2 | semidirect |
| 6. #11746489 | C2 | semidirect |
| 7. #11746488 | C2 | semidirect |
| 21. C4⋊(C3⋊#170) | C22 | semidirect |
| 22. C4×C3⋊#170 | C22 | semidirect |
| 23. C3×C4⋊#170 | C22 | semidirect |
| 24. C3×C4×#170 | C22 | semidirect |
| 35. #64871 | D3 | semidirect |
| 91. C4⋊#170 | C2×D3 | semidirect |
| 93. C4×#170 | C2×D3 | semidirect |
| 111. C5×D12 | M16 | semidirect |
| 116. C3×D20 | M16 | semidirect |
| 262. D20 | ΓL(1,𝔽25) | semidirect |
| 322. D12 | #700 | semidirect |
| 389. C3×C5 | #1486 | semidirect |
| 458. C5 | #68172 | semidirect |
| 480. C3 | #10604404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11753840 | 2 |
| #11751922 | 2 |
| #11751797 | 2 |
| #11746742 | 2 |
| C3×#64871 | 2 |
| #11746489 | 2 |
| #11746488 | 2 |
| #10604404 | 3 |
| #68172 | 5 |