Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
420 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 96 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. #11756329 | C2 | semidirect |
| 5. C3×Q8⋊#168 | C2 | semidirect |
| 6. #11745860 | C2 | semidirect |
| 7. #11745845 | C2 | semidirect |
| 31. Q8⋊#168 | D3 | semidirect |
| 85. C3×C5×Q8 | SD16 | semidirect |
| 194. C5×Q8 | #204 | semidirect |
| 238. C3×Q8 | #687 | semidirect |
| 297. C3×C5 | #1626 | semidirect |
| 322. Q8 | #6659 | semidirect |
| 343. C5 | #68252 | semidirect |
| 358. C3 | #10601823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756329 | 2 |
| C5×#5027 | 2 |
| #11747086 | 2 |
| #11746906 | 2 |
| C3×Q8⋊#168 | 2 |
| #11745860 | 2 |
| #11745845 | 2 |
| #10601823 | 3 |
| #68252 | 5 |