Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
482 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11729792 | C2 | semidirect |
| 3. C2×#89357 | C2 | semidirect |
| 4. C2×Dic7⋊C16 | C2 | semidirect |
| 5. #11725612 | C2 | semidirect |
| 109. C2×Dic7 | D16 | semidirect |
| 218. C7 | #13448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D16 | 2 |
| #11729792 | 2 |
| C2×#89357 | 2 |
| C2×Dic7⋊C16 | 2 |
| #11725612 | 2 |
| #13448 | 7 |