Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 332 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 |
|---|---|---|
| 3. #10598828 | C3 | direct (N × H) |
| 15. C2×C3×C5×Q8 | C8 | semidirect |
| 58. C2×C5×Q8 | C3×C8 | semidirect |
| 84. C2×C3×Q8 | #170 | semidirect |
| 152. C2×Q8 | C3×#170 | semidirect |
| 162. C3×C5 | #1272 | semidirect |
| 201. C5 | C3×#1272 | semidirect |
| 213. C3 | #10598828 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65519 | 2 |
| C3×#64918 | 2 |
| #10598828 | 3 |
| C3×#1272 | 5 |