Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
498 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 99 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. #11740575 | C2 | semidirect |
| 3. C7×#1509 | C2 | semidirect |
| 4. #11728572 | C2 | semidirect |
| 5. #11727241 | C2 | semidirect |
| 6. #11725561 | C2 | semidirect |
| 7. #11725427 | C2 | semidirect |
| 12. #89839 | C4 | semidirect |
| 13. #89830 | C4 | semidirect |
| 87. #1509 | D7 | semidirect |
| 397. C7 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740591 | 2 |
| #11740575 | 2 |
| C7×#1509 | 2 |
| #11728572 | 2 |
| #11727241 | 2 |
| #11725561 | 2 |
| #11725427 | 2 |
| #9378 | 7 |