Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 3. C4×C7×Q16 | C2 | semidirect |
| 4. #89803 | C2 | semidirect |
| 5. #89659 | C2 | semidirect |
| 6. #89580 | C2 | semidirect |
| 7. #89471 | C2 | semidirect |
| 38. C7×Q16 | D4 | semidirect |
| 62. C4×Q16 | D7 | semidirect |
| 74. D28 | Q16 | direct (N × H) |
| 107. C2×D7 | C2×Q16 | semidirect |
| 111. C4×C7 | C2×Q16 | semidirect |
| 127. Q16 | D28 | direct (N × H) |
| 166. C7 | D4×Q16 | semidirect |
| 176. C4 | D7×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×Q16 | 2 |
| Q8×D28 | 2 |
| C4×C7×Q16 | 2 |
| #89803 | 2 |
| #89659 | 2 |
| #89580 | 2 |
| #89471 | 2 |
| C8×D28 | 2 |
| D4×Q16 | 7 |