Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
318 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 37. C2×C7×C16 | Q8 | semidirect |
| 45. #6391 | Q8 | semidirect |
| 51. C2×C7⋊C16 | Q8 | semidirect |
| 142. C2×C16 | Dic14 | semidirect |
| 222. C7 | #13459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736616 | 2 |
| C7×#2155 | 2 |
| #11728459 | 2 |
| #11728439 | 2 |
| #11725624 | 2 |
| #11725617 | 2 |
| #11725531 | 2 |
| #13459 | 7 |