Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
854 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 203 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. C2×#89927 | C2 | semidirect |
| 3. C22×#6401 | C2 | semidirect |
| 4. C22×Dic56 | C2 | semidirect |
| 5. #11729219 | C2 | direct (N × H) |
| 6. C2×C16×Dic7 | C2 | semidirect |
| 15. #89927 | C22 | semidirect |
| 17. C2×#6401 | C22 | semidirect |
| 21. C2×Dic56 | C22 | semidirect |
| 22. C16×Dic7 | C22 | semidirect |
| 194. C2×C7 | #2249 | semidirect |
| 219. C7 | C2×#2249 | semidirect |
| 232. C2 | #11729219 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D16 | 2 |
| C2×#89927 | 2 |
| C22×#6401 | 2 |
| C22×Dic56 | 2 |
| #11729219 | 2 |
| C2×C16×Dic7 | 2 |
| C2×#2249 | 7 |