Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
234 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 75 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. #11725819 | C2 | semidirect |
| 4. #11725281 | C2 | semidirect |
| 5. #11725246 | C2 | semidirect |
| 44. C7×D8 | Q16 | semidirect |
| 124. D8 | Dic28 | semidirect |
| 161. C7 | #12445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C8×D8 | 2 |
| #11728640 | 2 |
| #11725819 | 2 |
| #11725281 | 2 |
| #11725246 | 2 |
| #12445 | 7 |