Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
568 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11729346 | C2 | semidirect |
| 3. #11729325 | C2 | semidirect |
| 4. #11725451 | C2 | semidirect |
| 5. C2×C7×#127 | C4 | semidirect |
| 10. C7×#394 | C4 | semidirect |
| 14. C7×#382 | C4 | semidirect |
| 100. C2×#127 | Dic7 | semidirect |
| 106. #394 | Dic7 | semidirect |
| 110. #382 | Dic7 | semidirect |
| 318. C7 | #11693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2619 | 2 |
| #11729346 | 2 |
| #11729325 | 2 |
| #11725451 | 2 |
| #11693 | 7 |