Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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. #11736616 | C2 | semidirect |
| 5. #11725628 | C2 | semidirect |
| 6. #11725617 | C2 | semidirect |
| 7. #11725533 | C2 | semidirect |
| 29. C2×C7×Q16 | Q8 | semidirect |
| 31. C2×C7×D8 | Q8 | semidirect |
| 157. C2×Q16 | Dic14 | semidirect |
| 159. C2×D8 | Dic14 | semidirect |
| 277. C7 | #13373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736616 | 2 |
| C7×#2145 | 2 |
| #11729839 | 2 |
| #11729830 | 2 |
| #11725628 | 2 |
| #11725617 | 2 |
| #11725533 | 2 |
| #13373 | 7 |