Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 332 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 |
|---|---|---|
| 1. C2×C7×#365 | C2 | semidirect |
| 3. C2×#89306 | C2 | semidirect |
| 5. #11728314 | C2 | semidirect |
| 7. #11725536 | C2 | semidirect |
| 56. C2×#365 | D7 | semidirect |
| 274. C7 | #13467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#365 | 2 |
| C2×#89313 | 2 |
| C2×#89306 | 2 |
| #11728450 | 2 |
| #11728314 | 2 |
| C2×#89283 | 2 |
| #11725536 | 2 |
| #13467 | 7 |