Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
200 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 55 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×#89315 | C2 | semidirect |
| 3. C2×#89242 | C2 | semidirect |
| 4. #11727082 | C2 | semidirect |
| 5. C7×#1415 | C2 | semidirect |
| 6. #11725403 | C2 | semidirect |
| 7. #11725381 | C2 | semidirect |
| 40. C7⋊C32 | D4 | semidirect |
| 47. #1415 | D7 | semidirect |
| 172. C7 | #13699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729223 | 2 |
| C2×#89315 | 2 |
| C2×#89242 | 2 |
| #11727082 | 2 |
| C7×#1415 | 2 |
| #11725403 | 2 |
| #11725381 | 2 |
| #13699 | 7 |