Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1350 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 447 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×D4×C7⋊C8 | C2 | semidirect |
| 3. #11729368 | C2 | semidirect |
| 4. #11727148 | C2 | semidirect |
| 5. C42×C7⋊C8 | C2 | semidirect |
| 20. C7×#127 | C8 | semidirect |
| 35. C4×C7⋊C8 | D4 | semidirect |
| 44. C2×C7×D4 | C2×C8 | semidirect |
| 54. C42×C7 | C2×C8 | semidirect |
| 90. C7⋊C8 | #127 | direct (N × H) |
| 97. #127 | C7⋊C8 | direct (N × H) |
| 117. C4×C7 | C8×D4 | semidirect |
| 123. C2×D4 | C2×C7⋊C8 | semidirect |
| 138. C42 | C2×C7⋊C8 | semidirect |
| 163. C7 | C8×#127 | semidirect |
| 172. C4 | D4×C7⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×#127 | 2 |
| C2×D4×C7⋊C8 | 2 |
| #11729368 | 2 |
| #11727148 | 2 |
| C42×C7⋊C8 | 2 |
| C8×#127 | 7 |