Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1022 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1022 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. C22×C7×D16 | C2 | semidirect |
| 2. C2×#89923 | C2 | semidirect |
| 3. C22×#6400 | C2 | semidirect |
| 4. C22×D112 | C2 | semidirect |
| 5. #11729218 | C2 | direct (N × H) |
| 6. C2×C16×Dic7 | C2 | semidirect |
| 12. C2×C7×D16 | C22 | semidirect |
| 15. #89923 | C22 | semidirect |
| 17. C2×#6400 | C22 | semidirect |
| 21. C2×D112 | C22 | semidirect |
| 22. C16×Dic7 | C22 | semidirect |
| 43. C2×C7×C16 | D4 | semidirect |
| 48. C2×C7⋊C16 | D4 | semidirect |
| 53. C22×D16 | D7 | semidirect |
| 86. C7×C16 | C2×D4 | semidirect |
| 87. C7⋊C16 | C2×D4 | semidirect |
| 97. C2×D16 | C2×D7 | semidirect |
| 119. C2×Dic7 | D16 | semidirect |
| 151. C2×C16 | C22⋊D7 | semidirect |
| 167. Dic7 | C2×D16 | semidirect |
| 198. C16 | C2×C22⋊D7 | semidirect |
| 200. C2×C7 | #2246 | semidirect |
| 228. C7 | C2×#2246 | semidirect |
| 244. C2 | #11729218 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D16 | 2 |
| C2×#89923 | 2 |
| C22×#6400 | 2 |
| C22×D112 | 2 |
| #11729218 | 2 |
| C2×C16×Dic7 | 2 |
| C2×#2246 | 7 |