Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
344 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 344 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 |
|---|---|---|
| 2. #11729616 | C2 | semidirect |
| 3. #11729614 | C2 | semidirect |
| 4. #11725603 | C2 | semidirect |
| 5. #11725588 | C2 | semidirect |
| 6. C7×#540 | C4 | semidirect |
| 9. C7×#493 | C4 | semidirect |
| 10. C7×#490 | C4 | semidirect |
| 16. C7×#433 | C4 | semidirect |
| 31. C7×#127 | C2×C4 | semidirect |
| 33. C7×#125 | C2×C4 | semidirect |
| 51. C7×#97 | C2×C4 | semidirect |
| 52. C4×C7×C8 | C2×C4 | semidirect |
| 101. #540 | Dic7 | semidirect |
| 104. #493 | Dic7 | semidirect |
| 105. #490 | Dic7 | semidirect |
| 111. #433 | Dic7 | semidirect |
| 161. #127 | C2×Dic7 | semidirect |
| 163. #125 | C2×Dic7 | semidirect |
| 184. #97 | C2×Dic7 | semidirect |
| 185. C4×C8 | C2×Dic7 | semidirect |
| 288. C7 | #13605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3220 | 2 |
| #11729616 | 2 |
| #11729614 | 2 |
| #11725603 | 2 |
| #11725588 | 2 |
| #13605 | 7 |