Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
390 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 390 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×#3283 | C2 | semidirect |
| 2. #11729067 | C2 | semidirect |
| 3. #11728643 | C2 | semidirect |
| 4. #11728601 | C2 | semidirect |
| 5. #11725599 | C2 | semidirect |
| 6. #11725569 | C2 | semidirect |
| 7. D4⋊(C7⋊C16) | C2 | semidirect |
| 57. #3283 | D7 | semidirect |
| 81. C7×D8 | D8 | semidirect |
| 221. D8 | #1141 | semidirect |
| 276. C7 | #12319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3283 | 2 |
| #11729067 | 2 |
| #11728643 | 2 |
| #11728601 | 2 |
| #11725599 | 2 |
| #11725569 | 2 |
| D4⋊(C7⋊C16) | 2 |
| #12319 | 7 |