Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
246 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 52. C7⋊C16 | Q16 | semidirect |
| 128. C7 | #12524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1713 | 2 |
| #11729139 | 2 |
| #11729138 | 2 |
| #11725818 | 2 |
| #11725243 | 2 |
| #12524 | 7 |