Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 344 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. C8×Dic30 | C2 | semidirect |
| 4. #11746946 | C2 | semidirect |
| 5. C3×#64677 | C2 | semidirect |
| 6. #11745857 | C2 | semidirect |
| 31. #64677 | D3 | semidirect |
| 81. Dic30 | SD16 | semidirect |
| 91. C3×C5×C8 | SD16 | semidirect |
| 184. C5×C8 | #204 | semidirect |
| 226. C3×C8 | #687 | semidirect |
| 259. C3×C5 | #1666 | semidirect |
| 296. C8 | #6659 | semidirect |
| 301. C5 | #68546 | semidirect |
| 314. C3 | #10602065 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic30 | 2 |
| C5×#4693 | 2 |
| #11747086 | 2 |
| #11746946 | 2 |
| C3×#64677 | 2 |
| #11745857 | 2 |
| #11745853 | 2 |
| #10602065 | 3 |
| #68546 | 5 |