Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1202 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 395 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. #11739905 | C2 | semidirect |
| 3. #11739880 | C2 | semidirect |
| 4. #11729568 | C2 | semidirect |
| 5. #11729565 | C2 | semidirect |
| 7. C7×#550 | C4 | semidirect |
| 8. C7×D4×Q8 | C4 | semidirect |
| 86. #550 | Dic7 | semidirect |
| 87. D4×Q8 | Dic7 | semidirect |
| 231. C7 | #17618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3497 | 2 |
| #11739905 | 2 |
| #11739880 | 2 |
| #11729568 | 2 |
| #11729565 | 2 |
| #17618 | 7 |