Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 486 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. #11739452 | C2 | semidirect |
| 3. C2×C7×#361 | C2 | semidirect |
| 4. C2×#89358 | C2 | semidirect |
| 5. #11728472 | C2 | semidirect |
| 6. #11725628 | C2 | semidirect |
| 7. #11725541 | C2 | semidirect |
| 51. C7×M32 | D4 | semidirect |
| 63. #6386 | D4 | semidirect |
| 70. C2×#361 | D7 | semidirect |
| 199. M32 | C22⋊D7 | semidirect |
| 314. C7 | #13079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741281 | 2 |
| #11739452 | 2 |
| C2×C7×#361 | 2 |
| C2×#89358 | 2 |
| #11728472 | 2 |
| #11725628 | 2 |
| #11725541 | 2 |
| #13079 | 7 |