Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
532 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 119 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. C7×#2112 | C2 | semidirect |
| 3. C2×C22⋊(C7⋊C16) | C2 | semidirect |
| 4. #11725328 | C2 | semidirect |
| 52. #2112 | D7 | semidirect |
| 298. C7 | #11419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89882 | 2 |
| C7×#2112 | 2 |
| C2×C22⋊(C7⋊C16) | 2 |
| #11725328 | 2 |
| #11419 | 7 |