Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
814 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 814 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. #11726820 | C2 | direct (N × H) |
| 67. C2×C4×C7 | Q32 | semidirect |
| 102. C4×C7 | C2×Q32 | semidirect |
| 125. C2×C7 | #2247 | semidirect |
| 134. C2×C4 | Dic56 | semidirect |
| 143. C7 | C2×#2247 | semidirect |
| 149. C4 | C2×Dic56 | semidirect |
| 152. C2 | #11726820 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic56 | 2 |
| C2×#89471 | 2 |
| C2×C4×C7×C16 | 2 |
| #11726820 | 2 |
| C2×#2247 | 7 |