Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
290 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 59 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×#2089 | C2 | semidirect |
| 3. #11728357 | C2 | semidirect |
| 5. #11725524 | C2 | semidirect |
| 6. #11725294 | C2 | semidirect |
| 64. #2089 | D7 | semidirect |
| 263. C7 | #12297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736542 | 2 |
| C7×#2089 | 2 |
| #11728357 | 2 |
| #11728353 | 2 |
| #11725524 | 2 |
| #11725294 | 2 |
| #11725293 | 2 |
| #12297 | 7 |