Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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×#6482 | C2 | semidirect |
| 2. C2×C7×SD32 | C2 | semidirect |
| 3. #89929 | C2 | semidirect |
| 4. C2×#6400 | C2 | semidirect |
| 5. #89359 | C2 | semidirect |
| 6. #89304 | C2 | semidirect |
| 7. (C2×D7)⋊C16 | C2 | semidirect |
| 34. C7×Q16 | D4 | semidirect |
| 43. D56 | D4 | semidirect |
| 49. C2×SD32 | D7 | semidirect |
| 116. Q16 | C22⋊D7 | semidirect |
| 157. C7 | #2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6482 | 2 |
| C2×C7×SD32 | 2 |
| #89929 | 2 |
| C2×#6400 | 2 |
| #89359 | 2 |
| #89304 | 2 |
| (C2×D7)⋊C16 | 2 |
| #2186 | 7 |