Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 116 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. C4⋊(C3⋊#674) | C2 | semidirect |
| 4. C3×C4⋊#674 | C2 | semidirect |
| 5. #11746563 | C2 | semidirect |
| 22. C4⋊#674 | D3 | semidirect |
| 107. C3×C4×C5 | M32 | semidirect |
| 112. Dic15 | M32 | semidirect |
| 180. C4×C5 | #798 | semidirect |
| 202. C3×C5 | #2150 | semidirect |
| 208. C3×C4 | #3990 | semidirect |
| 238. C5 | #69284 | semidirect |
| 247. C4 | #91166 | semidirect |
| 250. C3 | #10603827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91166 | 2 |
| C4×#6648 | 2 |
| C4⋊(C3⋊#674) | 2 |
| C3×C4⋊#674 | 2 |
| #11746563 | 2 |
| #10603827 | 3 |
| #69284 | 5 |