Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 113 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×C7×#358 | C2 | semidirect |
| 4. C2×#89360 | C2 | semidirect |
| 6. #11725614 | C2 | semidirect |
| 7. #11725529 | C2 | semidirect |
| 15. #89964 | C4 | semidirect |
| 73. C2×#358 | D7 | semidirect |
| 319. C7 | #13072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89964 | 2 |
| C2×#89673 | 2 |
| C2×C7×#358 | 2 |
| C2×#89360 | 2 |
| #11728400 | 2 |
| #11725614 | 2 |
| #11725529 | 2 |
| #13072 | 7 |