Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 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. C2×#89306 | C2 | semidirect |
| 4. C2×#89291 | C2 | semidirect |
| 5. #11728381 | C2 | semidirect |
| 7. C7×#1387 | C2 | semidirect |
| 72. #1387 | D7 | semidirect |
| 314. C7 | #13446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89681 | 2 |
| C2×#89306 | 2 |
| #11728450 | 2 |
| C2×#89291 | 2 |
| #11728381 | 2 |
| #11728352 | 2 |
| C7×#1387 | 2 |
| #13446 | 7 |