Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
182 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. C7×#1425 | C2 | semidirect |
| 4. #11725399 | C2 | semidirect |
| 5. #11725387 | C2 | semidirect |
| 33. #1425 | D7 | direct (N × H) |
| 110. D7 | #1425 | direct (N × H) |
| 124. C7 | C2×#1425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×C32 | 2 |
| D7×#368 | 2 |
| C7×#1425 | 2 |
| #11725399 | 2 |
| #11725387 | 2 |
| C2×#1425 | 7 |