Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C2×#89244 | C2 | semidirect |
| 2. C2×#89242 | C2 | semidirect |
| 3. #11727082 | C2 | semidirect |
| 5. C7×#1423 | C2 | semidirect |
| 6. #11725384 | C2 | semidirect |
| 7. #11725383 | C2 | semidirect |
| 39. C7×C32 | D4 | semidirect |
| 45. #1423 | D7 | semidirect |
| 116. C32 | D28 | semidirect |
| 172. C7 | #13699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89244 | 2 |
| C2×#89242 | 2 |
| #11727082 | 2 |
| #11727081 | 2 |
| C7×#1423 | 2 |
| #11725384 | 2 |
| #11725383 | 2 |
| #13699 | 7 |