Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
474 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 91 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. #11735969 | C2 | semidirect |
| 3. #11728538 | C2 | semidirect |
| 4. #11728517 | C2 | semidirect |
| 5. #11727614 | C2 | semidirect |
| 6. C7×#1299 | C2 | semidirect |
| 7. #11725522 | C2 | semidirect |
| 90. #1299 | D7 | semidirect |
| 386. C7 | #9349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736503 | 2 |
| #11735969 | 2 |
| #11728538 | 2 |
| #11728517 | 2 |
| #11727614 | 2 |
| C7×#1299 | 2 |
| #11725522 | 2 |
| #9349 | 7 |