Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
410 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 89. C2×C4×C7 | Q32 | semidirect |
| 190. C2×C4 | Dic56 | semidirect |
| 199. C7 | #13450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic56 | 2 |
| C2×C7×C4⋊C16 | 2 |
| C2×#89298 | 2 |
| #11727529 | 2 |
| #11725612 | 2 |
| #13450 | 7 |