Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
658 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 101 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. #11740624 | C2 | semidirect |
| 3. #11736512 | C2 | semidirect |
| 4. C7×#1545 | C2 | semidirect |
| 5. #11728543 | C2 | semidirect |
| 6. #11728521 | C2 | semidirect |
| 7. #11725521 | C2 | semidirect |
| 83. #1545 | D7 | semidirect |
| 121. C2×Dic14 | D8 | semidirect |
| 420. C7 | #10242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740624 | 2 |
| #11740611 | 2 |
| #11736512 | 2 |
| C7×#1545 | 2 |
| #11728543 | 2 |
| #11728521 | 2 |
| #11725521 | 2 |
| #10242 | 7 |