Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
866 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 251 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×#89865 | C2 | semidirect |
| 4. C2×#89452 | C2 | semidirect |
| 5. #11729010 | C2 | direct (N × H) |
| 6. C2×C8×C7⋊C8 | C2 | semidirect |
| 17. #89865 | C22 | semidirect |
| 23. #89452 | C22 | semidirect |
| 24. C8×C7⋊C8 | C22 | semidirect |
| 207. C2×C7 | #1708 | semidirect |
| 234. C7 | C2×#1708 | semidirect |
| 248. C2 | #11729010 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#492 | 2 |
| C2×#89865 | 2 |
| C2×#89842 | 2 |
| C2×#89452 | 2 |
| #11729010 | 2 |
| C2×C8×C7⋊C8 | 2 |
| C2×#1708 | 7 |