Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
930 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 219 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. C2×C7×#495 | C2 | semidirect |
| 2. C22×#6402 | C2 | semidirect |
| 3. C22×#6400 | C2 | semidirect |
| 4. C2×#89467 | C2 | semidirect |
| 5. #11729075 | C2 | direct (N × H) |
| 6. C2×#89256 | C2 | semidirect |
| 15. C7×#495 | C22 | semidirect |
| 18. C2×#6402 | C22 | semidirect |
| 20. C2×#6400 | C22 | semidirect |
| 23. #89467 | C22 | semidirect |
| 24. #89256 | C22 | semidirect |
| 56. C2×C7⋊C16 | D4 | semidirect |
| 60. C2×#495 | D7 | semidirect |
| 100. C7⋊C16 | C2×D4 | semidirect |
| 114. #495 | C2×D7 | semidirect |
| 231. C2×C7 | #2250 | semidirect |
| 263. C7 | C2×#2250 | semidirect |
| 280. C2 | #11729075 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#495 | 2 |
| C22×#6402 | 2 |
| C22×#6400 | 2 |
| C2×#89467 | 2 |
| #11729075 | 2 |
| C2×#89256 | 2 |
| C2×#2250 | 7 |