Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
294 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 20. Dic7⋊C16 | C4 | semidirect |
| 212. C7 | #13184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89308 | 2 |
| #11729174 | 2 |
| Dic7×#108 | 2 |
| #11728309 | 2 |
| C2×#89282 | 2 |
| C7×#1383 | 2 |
| #11725536 | 2 |
| #13184 | 7 |