Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
918 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 251 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. C22×#6401 | C2 | semidirect |
| 3. C2×#89471 | C2 | semidirect |
| 4. #11729045 | C2 | direct (N × H) |
| 5. C2×C4×C7⋊C16 | C2 | semidirect |
| 16. C2×#6401 | C22 | semidirect |
| 19. #89471 | C22 | semidirect |
| 20. C4×C7⋊C16 | C22 | semidirect |
| 46. C2×C7⋊C16 | D4 | semidirect |
| 81. C7⋊C16 | C2×D4 | semidirect |
| 105. C2×C4×C7 | SD32 | semidirect |
| 152. C4×C7 | C2×SD32 | semidirect |
| 186. C2×C7 | #2248 | semidirect |
| 202. C2×C4 | #6401 | semidirect |
| 211. C7 | C2×#2248 | semidirect |
| 220. C4 | C2×#6401 | semidirect |
| 224. C2 | #11729045 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#493 | 2 |
| C22×#6401 | 2 |
| C2×#89471 | 2 |
| #11729045 | 2 |
| C2×C4×C7⋊C16 | 2 |
| C2×#2248 | 7 |