Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 336 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. #11752447 | C2 | semidirect |
| 4. #11746801 | C2 | semidirect |
| 6. #11746755 | C2 | semidirect |
| 7. #11746751 | C2 | semidirect |
| 252. C3×C5 | #1585 | semidirect |
| 293. C5 | #70897 | semidirect |
| 306. C3 | #10604811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752447 | 2 |
| D4×C3⋊#170 | 2 |
| C3×SD16×Dic5 | 2 |
| #11746801 | 2 |
| D4⋊(C3⋊#170) | 2 |
| #11746755 | 2 |
| #11746751 | 2 |
| #10604811 | 3 |
| #70897 | 5 |