Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
596 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. C7×#1767 | C2 | semidirect |
| 3. C2×#89259 | C2 | semidirect |
| 4. #11727143 | C2 | semidirect |
| 49. #6377 | D4 | semidirect |
| 51. #1767 | D7 | semidirect |
| 291. C7 | #9689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11730758 | 2 |
| C7×#1767 | 2 |
| C2×#89259 | 2 |
| #11727143 | 2 |
| #9689 | 7 |