Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
624 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 624 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 |
|---|---|---|
| 2. #11751921 | C2 | semidirect |
| 3. #11751795 | C2 | semidirect |
| 4. D4⋊(C3⋊#170) | C2 | semidirect |
| 5. C3×D4⋊#170 | 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. D4⋊#170 | D3 | semidirect |
| 91. C4⋊#170 | C2×D3 | semidirect |
| 93. C4×#170 | C2×D3 | semidirect |
| 102. C3×C5×D4 | M16 | semidirect |
| 111. C5×D12 | M16 | semidirect |
| 251. C5×D4 | ΓL(1,𝔽25) | semidirect |
| 308. C3×D4 | #704 | semidirect |
| 322. D12 | #704 | semidirect |
| 389. C3×C5 | #1486 | semidirect |
| 427. D4 | #6739 | semidirect |
| 458. C5 | #68172 | semidirect |
| 480. C3 | #10604923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×D4×Dic5 | 2 |
| #11751921 | 2 |
| #11751795 | 2 |
| D4⋊(C3⋊#170) | 2 |
| C3×D4⋊#170 | 2 |
| #11746489 | 2 |
| #11746488 | 2 |
| #10604923 | 3 |
| #68172 | 5 |