Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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×SD32 | C2 | semidirect |
| 3. #89960 | C2 | semidirect |
| 4. C2×#6402 | C2 | semidirect |
| 5. #89357 | C2 | semidirect |
| 6. #89304 | C2 | semidirect |
| 7. (C2×D7)⋊C16 | C2 | semidirect |
| 9. C2×C7×Q16 | C22 | semidirect |
| 18. C2×C7×C16 | C22 | semidirect |
| 21. #6392 | C22 | semidirect |
| 22. C2×C7⋊C16 | C22 | semidirect |
| 50. C2×SD32 | D7 | semidirect |
| 78. C2×Q16 | C2×D7 | semidirect |
| 89. C2×C16 | C2×D7 | semidirect |
| 102. C2×D7 | SD32 | semidirect |
| 160. C7 | #2187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×D8 | 2 |
| C2×C7×SD32 | 2 |
| #89960 | 2 |
| C2×#6402 | 2 |
| #89357 | 2 |
| #89304 | 2 |
| (C2×D7)⋊C16 | 2 |
| #2187 | 7 |