Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
206 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #11725398 | C2 | direct (N × H) |
| 6. C2×C7×C32 | C4 | semidirect |
| 19. C7×C32 | C2×C4 | semidirect |
| 36. C2×C32 | Dic7 | semidirect |
| 58. C32 | C2×Dic7 | semidirect |
| 77. C2×C7 | #1424 | semidirect |
| 90. C7 | C2×#1424 | semidirect |
| 98. C2 | #11725398 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×C32 | 2 |
| C2×#89299 | 2 |
| #11725398 | 2 |
| C2×#1424 | 7 |