Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
640 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11740808 | C2 | semidirect |
| 2. #11740800 | C2 | semidirect |
| 4. C7×#1986 | C2 | semidirect |
| 5. #11727241 | C2 | semidirect |
| 6. #11727223 | C2 | semidirect |
| 7. #11725474 | C2 | semidirect |
| 82. #1986 | D7 | semidirect |
| 113. C7×M16 | SD16 | semidirect |
| 311. M16 | #1143 | semidirect |
| 387. C7 | #10194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740808 | 2 |
| #11740800 | 2 |
| #11735975 | 2 |
| C7×#1986 | 2 |
| #11727241 | 2 |
| #11727223 | 2 |
| #11725474 | 2 |
| #10194 | 7 |