Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
430 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 430 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 |
|---|---|---|
| 2. C2×C7×#358 | C2 | semidirect |
| 3. C2×#89360 | C2 | semidirect |
| 5. #11728379 | C2 | semidirect |
| 7. #11725611 | C2 | semidirect |
| 75. C2×#358 | D7 | semidirect |
| 337. C7 | #13412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741326 | 2 |
| C2×C7×#358 | 2 |
| C2×#89360 | 2 |
| C2×#89305 | 2 |
| #11728379 | 2 |
| #11728352 | 2 |
| #11725611 | 2 |
| #13412 | 7 |