Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
478 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 478 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 |
|---|---|---|
| 2. C2×#89679 | C2 | semidirect |
| 3. C2×C7×#361 | C2 | semidirect |
| 4. C2×#89357 | C2 | semidirect |
| 5. #11728475 | C2 | semidirect |
| 6. #11725623 | C2 | semidirect |
| 7. #11725534 | C2 | semidirect |
| 15. #89932 | C4 | semidirect |
| 72. C2×#361 | D7 | semidirect |
| 328. C7 | #13073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89932 | 2 |
| C2×#89679 | 2 |
| C2×C7×#361 | 2 |
| C2×#89357 | 2 |
| #11728475 | 2 |
| #11725623 | 2 |
| #11725534 | 2 |
| #13073 | 7 |