Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 1. C5×Q8×D12 | C2 | semidirect |
| 2. #11751128 | C2 | semidirect |
| 4. #11746912 | C2 | semidirect |
| 5. C3×Q8⋊#168 | C2 | semidirect |
| 6. #11745857 | C2 | semidirect |
| 7. #11745837 | C2 | semidirect |
| 32. Q8⋊#168 | D3 | semidirect |
| 60. Q8×D12 | D5 | semidirect |
| 88. C3×C5×Q8 | D8 | semidirect |
| 102. C5×D12 | SD16 | semidirect |
| 210. C5×Q8 | D24 | semidirect |
| 256. C3×Q8 | #686 | semidirect |
| 270. D12 | #688 | semidirect |
| 322. C3×C5 | #1627 | semidirect |
| 350. Q8 | #6654 | semidirect |
| 376. C5 | #68266 | semidirect |
| 393. C3 | #10602707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×D12 | 2 |
| #11751128 | 2 |
| #11747037 | 2 |
| #11746912 | 2 |
| C3×Q8⋊#168 | 2 |
| #11745857 | 2 |
| #11745837 | 2 |
| #10602707 | 3 |
| #68266 | 5 |