Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
334 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #11725588 | C2 | semidirect |
| 5. C7×#533 | C4 | semidirect |
| 9. C7×#488 | C4 | semidirect |
| 13. C4×C7×M16 | C4 | semidirect |
| 25. C7×#125 | C2×C4 | semidirect |
| 43. C4×C7×C8 | C2×C4 | semidirect |
| 88. #533 | Dic7 | semidirect |
| 92. #488 | Dic7 | semidirect |
| 98. C4×M16 | Dic7 | semidirect |
| 137. #125 | C2×Dic7 | semidirect |
| 158. C4×C8 | C2×Dic7 | semidirect |
| 248. C7 | #13603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3140 | 2 |
| C2×#89337 | 2 |
| C2×#89336 | 2 |
| #11725588 | 2 |
| #13603 | 7 |