Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
554 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 1. C7×#3156 | C2 | semidirect |
| 3. C22×#6402 | C2 | semidirect |
| 4. C2×#89362 | C2 | semidirect |
| 5. C2×#89360 | C2 | semidirect |
| 6. #11727657 | C2 | semidirect |
| 7. #11725477 | C2 | semidirect |
| 83. #3156 | D7 | semidirect |
| 377. C7 | #13337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3156 | 2 |
| C2×#89965 | 2 |
| C22×#6402 | 2 |
| C2×#89362 | 2 |
| C2×#89360 | 2 |
| #11727657 | 2 |
| #11725477 | 2 |
| #13337 | 7 |