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 |
|---|---|---|
| 2. C22×#6403 | C2 | semidirect |
| 4. C2×#89471 | C2 | semidirect |
| 5. #11729076 | C2 | direct (N × H) |
| 6. C2×#89256 | C2 | semidirect |
| 18. C2×#6403 | C22 | semidirect |
| 23. #89471 | C22 | semidirect |
| 24. #89256 | C22 | semidirect |
| 225. C2×C7 | #2251 | semidirect |
| 254. C7 | C2×#2251 | semidirect |
| 268. C2 | #11729076 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#495 | 2 |
| C22×#6403 | 2 |
| C22×#6401 | 2 |
| C2×#89471 | 2 |
| #11729076 | 2 |
| C2×#89256 | 2 |
| C2×#2251 | 7 |