Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
190 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11725407 | C2 | direct (N × H) |
| 8. C7×M64 | C4 | semidirect |
| 10. C2×C7×C32 | C4 | semidirect |
| 29. C7×C32 | C2×C4 | semidirect |
| 54. M64 | Dic7 | semidirect |
| 56. C2×C32 | Dic7 | semidirect |
| 88. C32 | C2×Dic7 | semidirect |
| 117. C2×C7 | #1426 | semidirect |
| 133. C7 | C2×#1426 | semidirect |
| 145. C2 | #11725407 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×M64 | 2 |
| C2×#89301 | 2 |
| C2×#89300 | 2 |
| #11725407 | 2 |
| C2×#1426 | 7 |