Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
548 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 105 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. #11731090 | C2 | semidirect |
| 3. C7×#1502 | C2 | semidirect |
| 4. #11729568 | C2 | semidirect |
| 5. #11728510 | C2 | semidirect |
| 6. #11725544 | C2 | semidirect |
| 7. #11725426 | C2 | semidirect |
| 14. #89855 | C4 | semidirect |
| 15. #89844 | C4 | semidirect |
| 76. #1502 | D7 | semidirect |
| 385. C7 | #9181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740742 | 2 |
| #11731090 | 2 |
| C7×#1502 | 2 |
| #11729568 | 2 |
| #11728510 | 2 |
| #11725544 | 2 |
| #11725426 | 2 |
| #9181 | 7 |