Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
5838 conjugacy classes of subgroups; only the 1339 normal subgroups are shown.
This group has 5838 conjugacy classes of subgroups — too many to draw. Only its 1339 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. C23×Dic7⋊C4 | C2 | semidirect |
| 3. C22×C7×#95 | C2 | semidirect |
| 4. C2×#89448 | C2 | direct (N × H) |
| 11. C22×Dic7⋊C4 | C22 | semidirect |
| 12. C2×C7×#95 | C22 | semidirect |
| 13. #89448 | C22 | direct (N × H) |
| 31. C2×Dic7⋊C4 | C23 | semidirect |
| 32. C7×#95 | C23 | semidirect |
| 36. C22×#95 | D7 | semidirect |
| 68. C2×#95 | C2×D7 | semidirect |
| 108. #95 | C22×D7 | semidirect |
| 109. C22×C7 | #396 | semidirect |
| 145. C2×C7 | C2×#396 | semidirect |
| 172. C7 | C22×#396 | semidirect |
| 177. C22 | #89448 | direct (N × H) |
| 187. C2 | C2×#89448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×(C2×D7)⋊C4 | 2 |
| C23×Dic7⋊C4 | 2 |
| C22×C7×#95 | 2 |
| C2×#89448 | 2 |
| C22×#396 | 7 |