Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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. C7×#3414 | C2 | semidirect |
| 2. #11741359 | C2 | semidirect |
| 3. #11729830 | C2 | semidirect |
| 4. #11729185 | C2 | semidirect |
| 5. #11725624 | C2 | semidirect |
| 28. C2×C7×Q16 | D4 | semidirect |
| 30. C2×C7×D8 | D4 | semidirect |
| 47. C2×C7×C16 | D4 | semidirect |
| 51. #6391 | D4 | semidirect |
| 54. #3414 | D7 | semidirect |
| 148. C2×Q16 | C22⋊D7 | semidirect |
| 150. C2×D8 | C22⋊D7 | semidirect |
| 169. C2×C16 | C22⋊D7 | semidirect |
| 263. C7 | #13309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3414 | 2 |
| #11741359 | 2 |
| #11729830 | 2 |
| #11729185 | 2 |
| #11725624 | 2 |
| #13309 | 7 |