Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
400 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 12. #91150 | C4 | semidirect |
| 13. ΓL(1,𝔽16)⋊C8 | C4 | semidirect |
| 14. #91099 | C4 | semidirect |
| 15. C5×C8×Dic3 | C4 | semidirect |
| 16. #90953 | C4 | semidirect |
| 17. #90951 | C4 | semidirect |
| 83. C8×Dic3 | AGL(1,𝔽5) | semidirect |
| 203. C3×C5 | #1747 | semidirect |
| 233. C5 | #68717 | semidirect |
| 243. C3 | #10603850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751696 | 2 |
| #11748050 | 2 |
| #11746766 | 2 |
| C3×#64897 | 2 |
| #11746520 | 2 |
| #10603850 | 3 |
| #68717 | 5 |