Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
386 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 87 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×#2138 | C2 | semidirect |
| 3. #11729840 | C2 | semidirect |
| 4. #11729166 | C2 | semidirect |
| 5. #11729155 | C2 | semidirect |
| 6. #11728412 | C2 | semidirect |
| 7. #11725531 | C2 | semidirect |
| 74. #2138 | D7 | semidirect |
| 331. C7 | #13447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741339 | 2 |
| C7×#2138 | 2 |
| #11729840 | 2 |
| #11729166 | 2 |
| #11729155 | 2 |
| #11728412 | 2 |
| #11725531 | 2 |
| #13447 | 7 |