Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
212 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 71 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. C4×C7×D16 | C2 | semidirect |
| 3. C4×D112 | C2 | semidirect |
| 4. #11725630 | C2 | semidirect |
| 5. #11725383 | C2 | semidirect |
| 6. #11725382 | C2 | semidirect |
| 7. #11725314 | C2 | semidirect |
| 15. #89314 | C4 | semidirect |
| 26. C7×D16 | C2×C4 | semidirect |
| 35. D112 | C2×C4 | semidirect |
| 37. C7⋊C32 | C2×C4 | semidirect |
| 40. C4×D16 | D7 | semidirect |
| 98. D16 | C4×D7 | semidirect |
| 160. C7 | #13654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×D16 | 2 |
| C2×#89314 | 2 |
| C4×D112 | 2 |
| #11725630 | 2 |
| #11725383 | 2 |
| #11725382 | 2 |
| #11725314 | 2 |
| #13654 | 7 |