Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
544 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. C7×#3215 | C2 | semidirect |
| 2. #11740806 | C2 | semidirect |
| 4. #11729579 | C2 | semidirect |
| 5. #11729474 | C2 | semidirect |
| 6. #11728555 | C2 | semidirect |
| 7. #11725559 | C2 | semidirect |
| 86. #3215 | D7 | semidirect |
| 375. C7 | #10121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3215 | 2 |
| #11740806 | 2 |
| #11740388 | 2 |
| #11729579 | 2 |
| #11729474 | 2 |
| #11728555 | 2 |
| #11725559 | 2 |
| #10121 | 7 |