Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
160 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. #11726800 | C2 | semidirect |
| 4. #11725388 | C2 | semidirect |
| 5. #11725316 | C2 | semidirect |
| 19. C7×Q32 | Q8 | semidirect |
| 21. C7×D16 | Q8 | semidirect |
| 76. Q32 | Dic14 | semidirect |
| 78. D16 | Dic14 | semidirect |
| 126. C7 | #13710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2178 | 2 |
| #11726800 | 2 |
| #11725634 | 2 |
| #11725388 | 2 |
| #11725316 | 2 |
| #13710 | 7 |