Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
340 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11726321 | C2 | semidirect |
| 4. C7×#1364 | C2 | semidirect |
| 5. #11725607 | C2 | semidirect |
| 6. #11725366 | C2 | semidirect |
| 7. #11725279 | C2 | semidirect |
| 57. #1364 | D7 | semidirect |
| 251. C7 | #11951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739378 | 2 |
| #11727029 | 2 |
| #11726321 | 2 |
| C7×#1364 | 2 |
| #11725607 | 2 |
| #11725366 | 2 |
| #11725279 | 2 |
| #11951 | 7 |