Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
822 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 331 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 |
|---|---|---|
| 37. C7×#97 | Q8 | semidirect |
| 38. C4×C7×C8 | Q8 | semidirect |
| 117. #97 | Dic14 | semidirect |
| 119. C4×C8 | Dic14 | semidirect |
| 174. C7 | #33317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89474 | 2 |
| #11730753 | 2 |
| #11730752 | 2 |
| C4×C7×#97 | 2 |
| #11727570 | 2 |
| #11727520 | 2 |
| #33317 | 7 |