Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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. Dic7×D16 | C2 | semidirect |
| 3. #11725630 | C2 | semidirect |
| 4. #11725398 | C2 | semidirect |
| 5. #11725395 | C2 | semidirect |
| 8. C7×D32 | C4 | semidirect |
| 18. C7×D16 | C2×C4 | semidirect |
| 24. C7×C32 | C2×C4 | semidirect |
| 45. D32 | Dic7 | semidirect |
| 64. D16 | C2×Dic7 | semidirect |
| 71. C32 | C2×Dic7 | semidirect |
| 105. C7 | #13654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×D32 | 2 |
| Dic7×D16 | 2 |
| #11725630 | 2 |
| #11725398 | 2 |
| #11725395 | 2 |
| #13654 | 7 |