Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #11729042 | C2 | semidirect |
| 3. #11728641 | C2 | semidirect |
| 4. #11728607 | C2 | semidirect |
| 5. #11725596 | C2 | semidirect |
| 6. #11725569 | C2 | semidirect |
| 7. D4⋊(C7⋊C16) | C2 | semidirect |
| 17. #89454 | C22 | semidirect |
| 22. C4⋊(C7⋊C16) | C22 | semidirect |
| 23. C4×C7⋊C16 | C22 | semidirect |
| 24. #89253 | C22 | semidirect |
| 273. C7 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D4×D8 | 2 |
| #11729042 | 2 |
| #11728641 | 2 |
| #11728607 | 2 |
| #11725596 | 2 |
| #11725569 | 2 |
| D4⋊(C7⋊C16) | 2 |
| #12372 | 7 |