Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
292 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. C7×#1366 | C2 | semidirect |
| 5. #11725606 | C2 | semidirect |
| 6. #11725380 | C2 | semidirect |
| 7. #11725379 | C2 | semidirect |
| 59. #1366 | D7 | semidirect |
| 220. C7 | #11956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739361 | 2 |
| D7×#364 | 2 |
| C7×#1366 | 2 |
| #11725606 | 2 |
| #11725380 | 2 |
| #11725379 | 2 |
| #11956 | 7 |