Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
556 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 556 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 |
|---|---|---|
| 1. C7×#3138 | C2 | semidirect |
| 2. #11740811 | C2 | semidirect |
| 4. #11729579 | C2 | semidirect |
| 5. #11729520 | C2 | semidirect |
| 6. #11727613 | C2 | semidirect |
| 7. #11725475 | C2 | semidirect |
| 79. #3138 | D7 | semidirect |
| 357. C7 | #10112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3138 | 2 |
| #11740811 | 2 |
| #11740611 | 2 |
| #11729579 | 2 |
| #11729520 | 2 |
| #11727613 | 2 |
| #11725475 | 2 |
| #10112 | 7 |