Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
584 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 145 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×C7×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #41×Dic7 | C2 | semidirect |
| 3. C2×#6512 | C2 | semidirect |
| 4. C2×#6503 | C2 | semidirect |
| 5. #89987 | C2 | semidirect |
| 6. #89935 | C2 | semidirect |
| 7. #89922 | C2 | semidirect |
| 8. #89903 | C2 | semidirect |
| 9. #89890 | C2 | semidirect |
| 15. C2×C7×SD16 | C22 | semidirect |
| 16. C2×C7×D8 | C22 | semidirect |
| 19. Q8×Dic7 | C22 | semidirect |
| 20. C2×#1143 | C22 | semidirect |
| 25. D4×Dic7 | C22 | semidirect |
| 26. C2×#1141 | C22 | semidirect |
| 32. #6406 | C22 | semidirect |
| 33. #6395 | C22 | semidirect |
| 34. Dic7⋊C8 | C22 | semidirect |
| 39. C7×#41 | D4 | semidirect |
| 76. C2×AGL(1,ℤ/8) | D7 | semidirect |
| 93. C7×Q8 | C2×D4 | semidirect |
| 99. C7×D4 | C2×D4 | semidirect |
| 125. C2×SD16 | C2×D7 | semidirect |
| 127. C2×D8 | C2×D7 | semidirect |
| 160. Dic7 | AGL(1,ℤ/8) | semidirect |
| 164. #41 | C22⋊D7 | semidirect |
| 215. Q8 | C2×C22⋊D7 | semidirect |
| 226. D4 | C2×C22⋊D7 | semidirect |
| 240. C7 | #3038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×AGL(1,ℤ/8) | 2 |
| #41×Dic7 | 2 |
| C2×#6512 | 2 |
| C2×#6503 | 2 |
| #89987 | 2 |
| #89935 | 2 |
| #89922 | 2 |
| #89903 | 2 |
| #89890 | 2 |
| #3038 | 7 |