Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
822 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 155 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×#2366 | C2 | semidirect |
| 3. C2×#89339 | C2 | semidirect |
| 4. #11727241 | C2 | semidirect |
| 5. #11725425 | C2 | semidirect |
| 14. #89845 | C4 | semidirect |
| 44. #6437 | C2×C4 | semidirect |
| 51. C4×C7⋊C8 | C2×C4 | semidirect |
| 53. #2366 | D7 | semidirect |
| 88. C7×C4⋊C4 | D8 | semidirect |
| 251. C4⋊C4 | #1141 | semidirect |
| 308. C7 | #9061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2366 | 2 |
| C2×#89845 | 2 |
| C2×#89339 | 2 |
| #11727241 | 2 |
| #11725425 | 2 |
| #9061 | 7 |