Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1022 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 251 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×#493 | C2 | semidirect |
| 2. C22×#6400 | C2 | semidirect |
| 3. C2×#89467 | C2 | semidirect |
| 4. #11729044 | C2 | direct (N × H) |
| 5. C2×C4×C7⋊C16 | C2 | semidirect |
| 13. C7×#493 | C22 | semidirect |
| 16. C2×#6400 | C22 | semidirect |
| 19. #89467 | C22 | semidirect |
| 20. C4×C7⋊C16 | C22 | semidirect |
| 46. C2×C7⋊C16 | D4 | semidirect |
| 50. C2×#493 | D7 | semidirect |
| 82. C7⋊C16 | C2×D4 | semidirect |
| 95. #493 | C2×D7 | semidirect |
| 109. C2×C4×C7 | D16 | semidirect |
| 158. C4×C7 | C2×D16 | semidirect |
| 192. C2×C7 | #2246 | semidirect |
| 211. C2×C4 | #6400 | semidirect |
| 220. C7 | C2×#2246 | semidirect |
| 231. C4 | C2×#6400 | semidirect |
| 236. C2 | #11729044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#493 | 2 |
| C22×#6400 | 2 |
| C2×#89467 | 2 |
| #11729044 | 2 |
| C2×C4×C7⋊C16 | 2 |
| C2×#2246 | 7 |