Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
462 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 101 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×#89362 | C2 | semidirect |
| 3. #11729832 | C2 | semidirect |
| 4. C2×#89358 | C2 | semidirect |
| 5. C2×#89357 | C2 | semidirect |
| 6. #11727648 | C2 | semidirect |
| 7. #11725477 | C2 | semidirect |
| 60. #6393 | D4 | semidirect |
| 350. C7 | #13411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3155 | 2 |
| C2×#89362 | 2 |
| #11729832 | 2 |
| C2×#89358 | 2 |
| C2×#89357 | 2 |
| #11727648 | 2 |
| #11725477 | 2 |
| #13411 | 7 |