Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3342 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 3342 conjugacy classes of subgroups — too many to draw. Only its 675 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×C7×#384 | C2 | semidirect |
| 3. C2×#89760 | C2 | semidirect |
| 4. C2×C42×Dic7 | C2 | semidirect |
| 12. C2×#6437 | C4 | semidirect |
| 34. C2×C4×Dic7 | D4 | semidirect |
| 38. C2×#384 | D7 | semidirect |
| 62. C42×C7 | C22⋊C4 | semidirect |
| 97. C2×Dic7 | #127 | semidirect |
| 131. C4×C7 | #390 | semidirect |
| 157. C42 | (C2×D7)⋊C4 | semidirect |
| 187. C7 | #14713 | semidirect |
| 202. C4 | #89760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6437 | 2 |
| C2×C7×#384 | 2 |
| C2×#89760 | 2 |
| C2×C42×Dic7 | 2 |
| #14713 | 7 |