Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
558 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 267 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 |
|---|---|---|
| 4. #11726800 | C2 | direct (N × H) |
| 23. C2×C7×C16 | Q8 | semidirect |
| 49. C7×C16 | C2×Q8 | semidirect |
| 80. C2×C16 | Dic14 | semidirect |
| 110. C16 | C2×Dic14 | semidirect |
| 111. C2×C7 | #2254 | semidirect |
| 127. C7 | C2×#2254 | semidirect |
| 136. C2 | #11726800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89454 | 2 |
| C2×C4×C7×C16 | 2 |
| C2×#89300 | 2 |
| #11726800 | 2 |
| C2×#2254 | 7 |