Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
444 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 2. #11731710 | C2 | semidirect |
| 4. #11728577 | C2 | semidirect |
| 6. C7×#1288 | C2 | semidirect |
| 7. #11725472 | C2 | semidirect |
| 17. #89466 | C4 | semidirect |
| 18. #89453 | C4 | semidirect |
| 68. #1288 | D7 | semidirect |
| 278. C7 | #9430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735973 | 2 |
| #11731710 | 2 |
| #11728589 | 2 |
| #11728577 | 2 |
| #11727318 | 2 |
| C7×#1288 | 2 |
| #11725472 | 2 |
| #9430 | 7 |