Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
434 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 107 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. C7×#1833 | C2 | semidirect |
| 4. C2×#89291 | C2 | semidirect |
| 6. #11728408 | C2 | semidirect |
| 7. #11727638 | C2 | semidirect |
| 18. #89471 | C4 | semidirect |
| 19. #89468 | C4 | semidirect |
| 74. #1833 | D7 | semidirect |
| 317. C7 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736021 | 2 |
| C7×#1833 | 2 |
| #11728444 | 2 |
| C2×#89291 | 2 |
| #11728410 | 2 |
| #11728408 | 2 |
| #11727638 | 2 |
| #13216 | 7 |