Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 101 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. Q8×Dic30 | C2 | semidirect |
| 5. #11746356 | C2 | semidirect |
| 6. #11746305 | C2 | semidirect |
| 7. #11746302 | C2 | semidirect |
| 86. C3×C5×Q8 | SD16 | semidirect |
| 103. Dic30 | SD16 | semidirect |
| 197. C5×Q8 | #214 | semidirect |
| 241. C3×Q8 | #687 | semidirect |
| 301. C3×C5 | #1623 | semidirect |
| 326. Q8 | #6716 | semidirect |
| 347. C5 | #71033 | semidirect |
| 362. C3 | #10601826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic30 | 2 |
| C3×C5×#460 | 2 |
| #11751177 | 2 |
| #11751176 | 2 |
| #11746356 | 2 |
| #11746305 | 2 |
| #11746302 | 2 |
| #10601826 | 3 |
| #71033 | 5 |