Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
826 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 219 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×#89676 | C2 | semidirect |
| 2. #11735912 | C2 | semidirect |
| 3. C2×C7×#346 | C2 | semidirect |
| 4. #11726838 | C2 | semidirect |
| 5. #11726835 | C2 | semidirect |
| 39. C2×C7×C16 | D4 | semidirect |
| 50. C2×#346 | D7 | semidirect |
| 130. C2×C16 | D28 | semidirect |
| 192. C7 | #33716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89676 | 2 |
| #11735912 | 2 |
| C2×C7×#346 | 2 |
| #11726838 | 2 |
| #11726835 | 2 |
| #33716 | 7 |