Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
356 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 29. C7×#107 | Q8 | semidirect |
| 37. #6386 | Q8 | semidirect |
| 110. #107 | Dic14 | semidirect |
| 173. C7 | #13457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89452 | 2 |
| C7×#1945 | 2 |
| C2×#89289 | 2 |
| #11725532 | 2 |
| #11725464 | 2 |
| #13457 | 7 |