Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1502 conjugacy classes of subgroups; only the 411 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 411 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. C22×#6377 | C2 | semidirect |
| 3. C2×#89335 | C2 | direct (N × H) |
| 13. C2×#6377 | C22 | semidirect |
| 14. #89335 | C22 | direct (N × H) |
| 38. #6377 | C23 | semidirect |
| 129. C22×C7 | #329 | semidirect |
| 167. C2×C7 | C2×#329 | semidirect |
| 192. C7 | C22×#329 | semidirect |
| 196. C22 | #89335 | direct (N × H) |
| 206. C2 | C2×#89335 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#124 | 2 |
| C22×#6377 | 2 |
| C2×#89335 | 2 |
| C22×#329 | 7 |