Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
366 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. C2×#89261 | C2 | semidirect |
| 3. #11725589 | C2 | direct (N × H) |
| 13. #89261 | C22 | semidirect |
| 150. C2×C7 | #1355 | semidirect |
| 172. C7 | C2×#1355 | semidirect |
| 189. C2 | #11725589 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#490 | 2 |
| C2×#89261 | 2 |
| #11725589 | 2 |
| C2×#1355 | 7 |