Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
410 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 111 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. C7×#2151 | C2 | semidirect |
| 3. #11729192 | C2 | semidirect |
| 4. #11729163 | C2 | semidirect |
| 5. #11727638 | C2 | semidirect |
| 47. #2151 | D7 | semidirect |
| 208. C7 | #13198 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736024 | 2 |
| C7×#2151 | 2 |
| #11729192 | 2 |
| #11729163 | 2 |
| #11727638 | 2 |
| #13198 | 7 |