Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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. C7×#2145 | C2 | semidirect |
| 4. C2×#89362 | C2 | semidirect |
| 5. #11728419 | C2 | semidirect |
| 6. #11725627 | C2 | semidirect |
| 7. #11725530 | C2 | semidirect |
| 14. #89964 | C4 | semidirect |
| 16. #89932 | C4 | semidirect |
| 75. #2145 | D7 | semidirect |
| 339. C7 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741373 | 2 |
| C2×#89679 | 2 |
| C7×#2145 | 2 |
| C2×#89362 | 2 |
| #11728419 | 2 |
| #11725627 | 2 |
| #11725530 | 2 |
| #13071 | 7 |