Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
158 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 22. C4×C7⋊C8 | C8 | semidirect |
| 131. C7 | #7366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11727301 | 2 |
| C7×#1324 | 2 |
| #11725438 | 2 |
| #7366 | 7 |