Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
492 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 492 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×#3140 | C2 | semidirect |
| 2. #11740803 | C2 | semidirect |
| 4. #11729581 | C2 | semidirect |
| 5. #11729474 | C2 | semidirect |
| 6. #11727607 | C2 | semidirect |
| 7. #11725476 | C2 | semidirect |
| 85. #3140 | D7 | semidirect |
| 363. C7 | #10124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3140 | 2 |
| #11740803 | 2 |
| #11740392 | 2 |
| #11729581 | 2 |
| #11729474 | 2 |
| #11727607 | 2 |
| #11725476 | 2 |
| #10124 | 7 |