Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
190 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11725385 | C2 | direct (N × H) |
| 12. #89294 | C4 | semidirect |
| 14. C2×C7⋊C32 | C4 | semidirect |
| 29. C7⋊C32 | C2×C4 | semidirect |
| 117. C2×C7 | #1426 | semidirect |
| 133. C7 | C2×#1426 | semidirect |
| 145. C2 | #11725385 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#367 | 2 |
| C2×#89301 | 2 |
| C2×#89294 | 2 |
| #11725385 | 2 |
| C2×#1426 | 7 |