Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
770 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11741519 | C2 | semidirect |
| 3. #11729893 | C2 | semidirect |
| 4. #11729428 | C2 | semidirect |
| 5. #11725422 | C2 | semidirect |
| 7. C2×C7×#127 | C4 | semidirect |
| 8. C2×C7×#124 | C4 | semidirect |
| 13. C7×#391 | C4 | semidirect |
| 14. C7×#390 | C4 | semidirect |
| 69. C22⋊(C7⋊C8) | D4 | semidirect |
| 145. C2×#127 | Dic7 | semidirect |
| 146. C2×#124 | Dic7 | semidirect |
| 155. #391 | Dic7 | semidirect |
| 156. #390 | Dic7 | semidirect |
| 447. C7 | #9445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2431 | 2 |
| #11741519 | 2 |
| #11729893 | 2 |
| #11729428 | 2 |
| #11725422 | 2 |
| #9445 | 7 |