Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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. #11727094 | C2 | semidirect |
| 5. #11725407 | C2 | semidirect |
| 6. #11725405 | C2 | semidirect |
| 7. #11725385 | C2 | semidirect |
| 23. C7×Q32 | Q8 | semidirect |
| 25. C7×D16 | Q8 | semidirect |
| 88. Q32 | Dic14 | semidirect |
| 90. D16 | Dic14 | semidirect |
| 143. C7 | #13710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729265 | 2 |
| #11727094 | 2 |
| C7×#1418 | 2 |
| #11725634 | 2 |
| #11725407 | 2 |
| #11725405 | 2 |
| #11725385 | 2 |
| #13710 | 7 |