Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
396 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 93 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×#2159 | C2 | semidirect |
| 3. C2×#89312 | C2 | semidirect |
| 6. C2×#89287 | C2 | semidirect |
| 7. #11725530 | C2 | semidirect |
| 70. #2159 | D7 | semidirect |
| 325. C7 | #13388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736629 | 2 |
| C7×#2159 | 2 |
| C2×#89312 | 2 |
| C2×#89310 | 2 |
| #11728400 | 2 |
| C2×#89287 | 2 |
| #11725530 | 2 |
| #13388 | 7 |