Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
800 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×C5×Q8×A4 | C2 | semidirect |
| 3. A4×#688 | C2 | direct (N × H) |
| 4. C2×A4×#168 | C2 | semidirect |
| 5. C23×#688 | C3 | semidirect |
| 8. C5×Q8×A4 | C22 | semidirect |
| 14. A4×#168 | C22 | semidirect |
| 16. C23×C5×Q8 | C2×C3 | semidirect |
| 23. C22×#688 | C2×C3 | semidirect |
| 24. C23×#168 | C2×C3 | semidirect |
| 35. C2×Q8×A4 | D5 | semidirect |
| 46. C22×C5×Q8 | C22×C3 | semidirect |
| 68. C2×#688 | A4 | direct (N × H) |
| 72. C22×#168 | C22×C3 | semidirect |
| 75. C2×C5×A4 | SD16 | semidirect |
| 87. Q8×A4 | C2×D5 | semidirect |
| 115. C2×C5×Q8 | C2×A4 | semidirect |
| 145. #688 | C2×A4 | direct (N × H) |
| 151. C2×#168 | C2×A4 | semidirect |
| 152. C23×Q8 | C3×D5 | semidirect |
| 164. C5×A4 | C2×SD16 | semidirect |
| 181. C23×C5 | C3×SD16 | semidirect |
| 204. C5×Q8 | C22×A4 | semidirect |
| 229. #168 | C22×A4 | semidirect |
| 237. C22×Q8 | C2×C3×D5 | semidirect |
| 269. C2×A4 | #688 | direct (N × H) |
| 285. C22×C5 | C2×C3×SD16 | semidirect |
| 324. C2×Q8 | D5×A4 | semidirect |
| 365. A4 | C2×#688 | direct (N × H) |
| 372. C2×C5 | A4×SD16 | semidirect |
| 393. C23 | C3×#688 | semidirect |
| 402. Q8 | C2×D5×A4 | semidirect |
| 431. C5 | C2×A4×SD16 | semidirect |
| 449. C22 | C2×C3×#688 | semidirect |
| 463. C2 | A4×#688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×A4 | 2 |
| C2×A4×D20 | 2 |
| A4×#688 | 2 |
| C2×A4×#168 | 2 |
| C23×#688 | 3 |
| C2×C3×#688 | 4 |
| C2×A4×SD16 | 5 |