Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
346 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 75 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×#3334 | C2 | semidirect |
| 2. #11729135 | C2 | semidirect |
| 3. #11728643 | C2 | semidirect |
| 4. #11728601 | C2 | semidirect |
| 5. #11725607 | C2 | semidirect |
| 6. #11725569 | C2 | semidirect |
| 7. D4⋊(C7⋊C16) | C2 | semidirect |
| 54. #3334 | D7 | semidirect |
| 122. C7×D4 | D16 | semidirect |
| 245. D4 | #6400 | semidirect |
| 262. C7 | #12340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3334 | 2 |
| #11729135 | 2 |
| #11728643 | 2 |
| #11728601 | 2 |
| #11725607 | 2 |
| #11725569 | 2 |
| D4⋊(C7⋊C16) | 2 |
| #12340 | 7 |