Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1770 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1770 conjugacy classes of subgroups — too many to draw. Only its 451 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 |
|---|---|---|
| 2. C2×#89709 | C2 | semidirect |
| 3. C2×C42×Dic7 | C2 | semidirect |
| 4. #11729318 | C2 | semidirect |
| 8. C2×C7×#126 | C4 | semidirect |
| 65. C42×C7 | C22⋊C4 | semidirect |
| 70. C2×#126 | Dic7 | semidirect |
| 103. C2×Dic7 | #126 | semidirect |
| 161. C42 | C22⋊Dic7 | semidirect |
| 191. C7 | #14711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#126 | 2 |
| C2×#89709 | 2 |
| C2×C42×Dic7 | 2 |
| #11729318 | 2 |
| #11729299 | 2 |
| #14711 | 7 |