Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
176 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11726798 | C2 | semidirect |
| 4. #11725382 | C2 | semidirect |
| 5. C4⋊(C7⋊C32) | C2 | semidirect |
| 20. C7×D16 | Q8 | semidirect |
| 75. D16 | Dic14 | semidirect |
| 126. C7 | #13705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×D16 | 2 |
| #11726798 | 2 |
| #11725630 | 2 |
| #11725382 | 2 |
| C4⋊(C7⋊C32) | 2 |
| #13705 | 7 |