Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
182 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #11729250 | C2 | semidirect |
| 5. #11725633 | C2 | semidirect |
| 6. #11725407 | C2 | semidirect |
| 7. #11725406 | C2 | semidirect |
| 12. C7×Q64 | C4 | semidirect |
| 13. C7×SD64 | C4 | semidirect |
| 70. Q64 | Dic7 | semidirect |
| 71. SD64 | Dic7 | semidirect |
| 155. C7 | #13657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2264 | 2 |
| #11729266 | 2 |
| #11729250 | 2 |
| #11725634 | 2 |
| #11725633 | 2 |
| #11725407 | 2 |
| #11725406 | 2 |
| #13657 | 7 |