Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
482 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 6. #11727095 | C2 | semidirect |
| 7. #11727076 | C2 | semidirect |
| 37. C2×C7×C16 | Q8 | semidirect |
| 46. C2×C7⋊C16 | Q8 | semidirect |
| 124. C2×C16 | Dic14 | semidirect |
| 184. C7 | #33728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736615 | 2 |
| C7×#2158 | 2 |
| #11729158 | 2 |
| C2×#89297 | 2 |
| #11728402 | 2 |
| #11727095 | 2 |
| #11727076 | 2 |
| #33728 | 7 |