Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11739452 | C2 | semidirect |
| 3. C7×#2145 | C2 | semidirect |
| 4. #11729830 | C2 | semidirect |
| 5. #11728418 | C2 | semidirect |
| 6. #11725625 | C2 | semidirect |
| 7. #11725532 | C2 | semidirect |
| 14. #89961 | C4 | semidirect |
| 16. #89931 | C4 | semidirect |
| 54. C7×M32 | D4 | semidirect |
| 65. #6386 | D4 | semidirect |
| 73. #2145 | D7 | semidirect |
| 213. M32 | C22⋊D7 | semidirect |
| 338. C7 | #13077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741361 | 2 |
| #11739452 | 2 |
| C7×#2145 | 2 |
| #11729830 | 2 |
| #11728418 | 2 |
| #11725625 | 2 |
| #11725532 | 2 |
| #13077 | 7 |