Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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×#362 | C2 | semidirect |
| 3. #11729820 | C2 | semidirect |
| 5. C2×#89306 | C2 | semidirect |
| 7. #11725538 | C2 | semidirect |
| 68. C2×#362 | D7 | semidirect |
| 314. C7 | #13446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89951 | 2 |
| C2×C7×#362 | 2 |
| #11729820 | 2 |
| #11729193 | 2 |
| C2×#89306 | 2 |
| #11728450 | 2 |
| #11725538 | 2 |
| #13446 | 7 |