Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
422 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#89312 | C2 | semidirect |
| 4. C2×#89312 | C2 | semidirect |
| 6. #11727655 | C2 | semidirect |
| 7. C7×#1378 | C2 | semidirect |
| 75. #1378 | D7 | semidirect |
| 318. C7 | #13418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736021 | 2 |
| #11729202 | 2 |
| C2×#89312 | 2 |
| #11729196 | 2 |
| #11727655 | 2 |
| C7×#1378 | 2 |
| #13418 | 7 |