Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3294 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 627 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×#399 | C2 | semidirect |
| 2. C2×#89766 | C2 | semidirect |
| 4. C2×#89721 | C2 | semidirect |
| 5. #11735573 | C2 | direct (N × H) |
| 6. C2×#89448 | C2 | semidirect |
| 8. C22×C7×C4⋊C4 | C22 | semidirect |
| 13. C22×C4⋊Dic7 | C22 | semidirect |
| 14. C22×Dic7⋊C4 | C22 | semidirect |
| 15. C7×#399 | C22 | semidirect |
| 16. C2×C7×#95 | C22 | semidirect |
| 17. C2×C7⋊#95 | C22 | semidirect |
| 18. #89766 | C22 | semidirect |
| 20. #89721 | C22 | semidirect |
| 21. #89448 | C22 | semidirect |
| 33. C2×C7×C4⋊C4 | C23 | semidirect |
| 43. C2×C4⋊Dic7 | C23 | semidirect |
| 45. C2×Dic7⋊C4 | C23 | semidirect |
| 46. C7×#95 | C23 | semidirect |
| 47. C7⋊#95 | C23 | semidirect |
| 50. C2×#399 | D7 | semidirect |
| 89. C22×C4⋊C4 | C2×D7 | semidirect |
| 95. #399 | C2×D7 | semidirect |
| 100. C2×#95 | C2×D7 | semidirect |
| 145. C2×C4⋊C4 | C22×D7 | semidirect |
| 155. #95 | C22×D7 | semidirect |
| 207. C2×C7 | #2842 | semidirect |
| 242. C7 | C2×#2842 | semidirect |
| 263. C2 | #11735573 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#399 | 2 |
| C2×#89766 | 2 |
| C2×#89727 | 2 |
| C2×#89721 | 2 |
| #11735573 | 2 |
| C2×#89448 | 2 |
| C2×#2842 | 7 |