Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
676 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 676 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×#1537 | C2 | semidirect |
| 3. #11729594 | C2 | semidirect |
| 4. #11728590 | C2 | semidirect |
| 6. #11728579 | C2 | semidirect |
| 9. #90423 | C4 | semidirect |
| 10. #90418 | C4 | semidirect |
| 95. #1537 | D7 | semidirect |
| 387. C7 | #8496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11743335 | 2 |
| C7×#1537 | 2 |
| #11729594 | 2 |
| #11728590 | 2 |
| #11728586 | 2 |
| #11728579 | 2 |
| #11728573 | 2 |
| #8496 | 7 |