Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
818 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 243 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. #11740720 | C2 | semidirect |
| 3. #11729841 | C2 | semidirect |
| 4. #11729570 | C2 | semidirect |
| 5. #11727595 | C2 | semidirect |
| 6. #11727560 | C2 | semidirect |
| 10. C7×#497 | C4 | semidirect |
| 11. C7×#496 | C4 | semidirect |
| 95. #497 | Dic7 | semidirect |
| 96. #496 | Dic7 | semidirect |
| 230. C7 | #22281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3150 | 2 |
| #11740720 | 2 |
| #11729841 | 2 |
| #11729570 | 2 |
| #11727595 | 2 |
| #11727560 | 2 |
| #22281 | 7 |