Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 110. C7⋊C8 | Q32 | semidirect |
| 189. C7 | #12421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2209 | 2 |
| #11729050 | 2 |
| #11728665 | 2 |
| Q16×C7⋊C8 | 2 |
| #11725599 | 2 |
| #11725371 | 2 |
| #11725360 | 2 |
| #12421 | 7 |