Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
158 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 14. C4×C7×C8 | C8 | semidirect |
| 58. C4×C8 | C7⋊C8 | semidirect |
| 102. C7 | #7366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1835 | 2 |
| #11725438 | 2 |
| #7366 | 7 |