Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
442 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 151 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×#346 | C2 | semidirect |
| 4. C4×#6393 | C2 | semidirect |
| 5. #11725613 | C2 | semidirect |
| 19. #89305 | C4 | semidirect |
| 39. C2×C7×C16 | C2×C4 | semidirect |
| 44. #6393 | C2×C4 | semidirect |
| 52. C2×#346 | D7 | semidirect |
| 143. C2×C16 | C4×D7 | semidirect |
| 226. C7 | #12640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6467 | 2 |
| C2×C7×#346 | 2 |
| C2×#89305 | 2 |
| C4×#6393 | 2 |
| #11725613 | 2 |
| #12640 | 7 |