Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2310 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2310 conjugacy classes of subgroups — too many to draw. Only its 747 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×#6433 | C2 | semidirect |
| 3. C22×#6409 | C2 | semidirect |
| 5. C2×#89828 | C2 | direct (N × H) |
| 6. C22×C4×C7⋊C8 | C2 | semidirect |
| 17. C2×#6433 | C22 | semidirect |
| 18. C2×#6409 | C22 | semidirect |
| 20. #89828 | C22 | direct (N × H) |
| 21. C2×C4×C7⋊C8 | C22 | semidirect |
| 45. #6433 | C23 | semidirect |
| 46. #6409 | C23 | semidirect |
| 48. C4×C7⋊C8 | C23 | semidirect |
| 150. C22×C7 | #488 | semidirect |
| 189. C2×C7 | C2×#488 | semidirect |
| 214. C7 | C22×#488 | semidirect |
| 218. C22 | #89828 | direct (N × H) |
| 228. C2 | C2×#89828 | 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×#6433 | 2 |
| C22×#6409 | 2 |
| C22×#6406 | 2 |
| C2×#89828 | 2 |
| C22×C4×C7⋊C8 | 2 |
| C22×#488 | 7 |