Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×Q8⋊#168 | C2 | semidirect |
| 6. #11745863 | C2 | semidirect |
| 7. #11745845 | C2 | semidirect |
| 31. Q8⋊#168 | D3 | semidirect |
| 86. C3×C5×Q8 | SD16 | semidirect |
| 98. Dic30 | SD16 | semidirect |
| 197. C5×Q8 | #204 | semidirect |
| 241. C3×Q8 | #687 | semidirect |
| 301. C3×C5 | #1623 | semidirect |
| 326. Q8 | #6659 | semidirect |
| 347. C5 | #68264 | 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 |
| C5×#5027 | 2 |
| #11747086 | 2 |
| #11747066 | 2 |
| C3×Q8⋊#168 | 2 |
| #11745863 | 2 |
| #11745845 | 2 |
| #10601826 | 3 |
| #68264 | 5 |