Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
690 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 105 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×#2858 | C2 | semidirect |
| 2. #11740658 | C2 | semidirect |
| 4. #11729528 | C2 | semidirect |
| 5. #11729513 | C2 | semidirect |
| 6. #11727149 | C2 | semidirect |
| 7. #11725417 | C2 | semidirect |
| 74. #2858 | D7 | semidirect |
| 351. C7 | #10281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2858 | 2 |
| #11740658 | 2 |
| #11740611 | 2 |
| #11729528 | 2 |
| #11729513 | 2 |
| #11727149 | 2 |
| #11725417 | 2 |
| #10281 | 7 |