Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
680 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 3. C22×Dic56 | C2 | semidirect |
| 4. #11736614 | C2 | semidirect |
| 6. #11729155 | C2 | semidirect |
| 7. #11728408 | C2 | semidirect |
| 8. #11726990 | C2 | semidirect |
| 9. #11726959 | C2 | semidirect |
| 325. C7 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741352 | 2 |
| C2×#89967 | 2 |
| C22×Dic56 | 2 |
| #11736614 | 2 |
| C7×#2138 | 2 |
| #11729155 | 2 |
| #11728408 | 2 |
| #11726990 | 2 |
| #11726959 | 2 |
| #33588 | 7 |