Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1618 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1618 conjugacy classes of subgroups — too many to draw. Only its 331 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×#89484 | C2 | semidirect |
| 2. C2×#89468 | C2 | semidirect |
| 3. C2×#89467 | C2 | semidirect |
| 4. #11730876 | C2 | semidirect |
| 5. C7×#1726 | C2 | semidirect |
| 38. C7×#97 | D4 | semidirect |
| 39. C4×C7×C8 | D4 | semidirect |
| 45. #1726 | D7 | semidirect |
| 116. #97 | D28 | semidirect |
| 117. C4×C8 | D28 | semidirect |
| 170. C7 | #33308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89484 | 2 |
| C2×#89468 | 2 |
| C2×#89467 | 2 |
| #11730876 | 2 |
| C7×#1726 | 2 |
| #33308 | 7 |