Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
392 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11727029 | C2 | semidirect |
| 3. #11726284 | C2 | semidirect |
| 4. C7×#1360 | C2 | semidirect |
| 5. #11725602 | C2 | semidirect |
| 6. #11725368 | C2 | semidirect |
| 7. #11725273 | C2 | semidirect |
| 71. #1360 | D7 | semidirect |
| 325. C7 | #11960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739265 | 2 |
| #11727029 | 2 |
| #11726284 | 2 |
| C7×#1360 | 2 |
| #11725602 | 2 |
| #11725368 | 2 |
| #11725273 | 2 |
| #11960 | 7 |