Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1126 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1126 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 1. C2×#90413 | C2 | semidirect |
| 4. C2×#89341 | C2 | semidirect |
| 5. #11729023 | C2 | direct (N × H) |
| 6. C2×#89251 | C2 | semidirect |
| 14. #90413 | C22 | semidirect |
| 25. #89341 | C22 | semidirect |
| 26. #89251 | C22 | semidirect |
| 93. C2×Dic14 | SD16 | semidirect |
| 161. Dic14 | C2×SD16 | semidirect |
| 259. C2×C7 | #1623 | semidirect |
| 292. C7 | C2×#1623 | semidirect |
| 308. C2 | #11729023 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90413 | 2 |
| C2×C7×#492 | 2 |
| C2×#89847 | 2 |
| C2×#89341 | 2 |
| #11729023 | 2 |
| C2×#89251 | 2 |
| C2×#1623 | 7 |