Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
412 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 79 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×#2165 | C2 | semidirect |
| 3. #11727618 | C2 | semidirect |
| 4. #11725377 | C2 | semidirect |
| 5. #11725376 | C2 | semidirect |
| 17. C7×#364 | C22 | semidirect |
| 22. #89258 | C22 | semidirect |
| 57. #2165 | D7 | semidirect |
| 112. #364 | C2×D7 | semidirect |
| 276. C7 | #11992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735975 | 2 |
| C7×#2165 | 2 |
| #11727618 | 2 |
| #11725377 | 2 |
| #11725376 | 2 |
| #11992 | 7 |