Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
850 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 175 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×#89339 | C2 | semidirect |
| 3. #11727146 | C2 | semidirect |
| 4. #11727145 | C2 | semidirect |
| 39. C4⋊(C7⋊C8) | D4 | semidirect |
| 229. C7 | #9706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2867 | 2 |
| C2×#89339 | 2 |
| #11727146 | 2 |
| #11727145 | 2 |
| #9706 | 7 |