Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
494 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×C7×#347 | C2 | semidirect |
| 4. C2×#89261 | C2 | semidirect |
| 5. #11725616 | C2 | semidirect |
| 18. #89309 | C4 | semidirect |
| 40. C7×M32 | C2×C4 | semidirect |
| 48. #6386 | C2×C4 | semidirect |
| 54. C2×#347 | D7 | semidirect |
| 155. M32 | C4×D7 | semidirect |
| 248. C7 | #12607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89479 | 2 |
| C2×C7×#347 | 2 |
| C2×#89309 | 2 |
| C2×#89261 | 2 |
| #11725616 | 2 |
| #12607 | 7 |