Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1154 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 203 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. #11740760 | C2 | semidirect |
| 3. #11739926 | C2 | semidirect |
| 4. #11729634 | C2 | semidirect |
| 5. #11729629 | C2 | semidirect |
| 6. #11729568 | C2 | semidirect |
| 7. #11729378 | C2 | semidirect |
| 100. C2×C7×Q8 | SD16 | semidirect |
| 282. C2×Q8 | #1142 | semidirect |
| 364. C7 | #18219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3497 | 2 |
| #11740760 | 2 |
| #11739926 | 2 |
| #11729634 | 2 |
| #11729629 | 2 |
| #11729568 | 2 |
| #11729378 | 2 |
| #18219 | 7 |