Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 226 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 |
|---|---|---|
| 1. C2×D7×Q16 | C2 | semidirect |
| 2. C2×C7×SD32 | C2 | semidirect |
| 4. C2×#6401 | C2 | semidirect |
| 5. #89359 | C2 | semidirect |
| 6. (C2×D7)⋊C16 | C2 | semidirect |
| 7. #89298 | C2 | semidirect |
| 34. C7×Q16 | D4 | semidirect |
| 43. Dic28 | D4 | semidirect |
| 50. C2×SD32 | D7 | semidirect |
| 97. C2×D7 | SD32 | semidirect |
| 117. Q16 | C22⋊D7 | semidirect |
| 154. C7 | #2185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×Q16 | 2 |
| C2×C7×SD32 | 2 |
| #89929 | 2 |
| C2×#6401 | 2 |
| #89359 | 2 |
| (C2×D7)⋊C16 | 2 |
| #89298 | 2 |
| #2185 | 7 |