Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
690 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 103 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. #11740696 | C2 | semidirect |
| 2. #11740658 | C2 | semidirect |
| 4. C7×#1548 | C2 | semidirect |
| 5. #11728266 | C2 | semidirect |
| 6. #11728256 | C2 | semidirect |
| 7. #11725542 | C2 | semidirect |
| 76. #1548 | 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 |
|---|---|
| #11740696 | 2 |
| #11740658 | 2 |
| #11736748 | 2 |
| C7×#1548 | 2 |
| #11728266 | 2 |
| #11728256 | 2 |
| #11725542 | 2 |
| #10281 | 7 |