Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
602 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 159 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×#89341 | C2 | semidirect |
| 4. #11727146 | C2 | semidirect |
| 5. C4×C4⋊(C7⋊C8) | C2 | semidirect |
| 246. C7 | #9699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2858 | 2 |
| C2×#89341 | 2 |
| C2×#89339 | 2 |
| #11727146 | 2 |
| C4×C4⋊(C7⋊C8) | 2 |
| #9699 | 7 |