Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
460 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 95 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. #11728281 | C2 | semidirect |
| 3. #11728252 | C2 | semidirect |
| 4. #11728244 | C2 | semidirect |
| 5. #11728186 | C2 | semidirect |
| 6. C2×#89278 | C2 | semidirect |
| 7. C7×#1292 | C2 | semidirect |
| 76. #1292 | D7 | semidirect |
| 369. C7 | #10457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736500 | 2 |
| #11728281 | 2 |
| #11728252 | 2 |
| #11728244 | 2 |
| #11728186 | 2 |
| C2×#89278 | 2 |
| C7×#1292 | 2 |
| #10457 | 7 |