Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
418 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 418 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. #11726860 | C2 | semidirect |
| 3. D7×C22⋊C16 | C2 | semidirect |
| 4. C7×#1322 | C2 | semidirect |
| 5. #11725515 | C2 | semidirect |
| 6. #11725328 | C2 | semidirect |
| 7. #11725328 | C2 | semidirect |
| 69. #1322 | D7 | semidirect |
| 344. C7 | #11467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89608 | 2 |
| #11726860 | 2 |
| D7×C22⋊C16 | 2 |
| C7×#1322 | 2 |
| #11725515 | 2 |
| #11725328 | 2 |
| #11467 | 7 |