Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 314 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×#3338 | C2 | semidirect |
| 2. #11729135 | C2 | semidirect |
| 3. #11728668 | C2 | semidirect |
| 5. #11725608 | C2 | semidirect |
| 6. #11725571 | C2 | semidirect |
| 7. D4⋊(C7⋊C16) | C2 | semidirect |
| 54. #3338 | D7 | semidirect |
| 117. C7×D4 | SD32 | semidirect |
| 231. D4 | #6402 | semidirect |
| 247. C7 | #12342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3338 | 2 |
| #11729135 | 2 |
| #11728668 | 2 |
| #11728601 | 2 |
| #11725608 | 2 |
| #11725571 | 2 |
| D4⋊(C7⋊C16) | 2 |
| #12342 | 7 |