Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
430 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 99 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×#1952 | C2 | semidirect |
| 4. C2×#89291 | C2 | semidirect |
| 5. C2×#89287 | C2 | semidirect |
| 7. #11725477 | C2 | semidirect |
| 76. #1952 | D7 | semidirect |
| 337. C7 | #13412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736021 | 2 |
| C7×#1952 | 2 |
| C2×#89292 | 2 |
| C2×#89291 | 2 |
| C2×#89287 | 2 |
| #11728352 | 2 |
| #11725477 | 2 |
| #13412 | 7 |