Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
514 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 155 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×#2252 | C2 | semidirect |
| 3. #11729136 | C2 | semidirect |
| 5. #11727072 | C2 | semidirect |
| 6. #11726820 | C2 | semidirect |
| 51. #2252 | D7 | semidirect |
| 113. C4×D7 | Q32 | semidirect |
| 209. C7 | #33734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739379 | 2 |
| C7×#2252 | 2 |
| #11729136 | 2 |
| #11727082 | 2 |
| #11727072 | 2 |
| #11726820 | 2 |
| C4×D7×C16 | 2 |
| #33734 | 7 |