Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
452 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 452 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. #11728537 | C2 | semidirect |
| 3. #11728526 | C2 | semidirect |
| 4. #11728247 | C2 | semidirect |
| 5. #11727310 | C2 | semidirect |
| 6. #11727299 | C2 | semidirect |
| 7. C7×#1286 | C2 | semidirect |
| 73. #1286 | D7 | semidirect |
| 351. C7 | #10465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736500 | 2 |
| #11728537 | 2 |
| #11728526 | 2 |
| #11728247 | 2 |
| #11727310 | 2 |
| #11727299 | 2 |
| C7×#1286 | 2 |
| #10465 | 7 |