Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
616 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 221 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×C4×C7×D4 | C2 | semidirect |
| 3. C2×C4×D28 | C2 | semidirect |
| 4. C2×#6406 | C2 | semidirect |
| 5. C4×#1141 | C2 | direct (N × H) |
| 6. C2×#6383 | C2 | semidirect |
| 7. C2×#6381 | C2 | semidirect |
| 8. C2×C4×C7⋊C8 | C2 | semidirect |
| 14. C4×C7×D4 | C22 | semidirect |
| 18. C2×#1141 | C4 | direct (N × H) |
| 25. C4×D28 | C22 | semidirect |
| 26. #6406 | C22 | semidirect |
| 27. #6383 | C22 | semidirect |
| 28. #6381 | C22 | semidirect |
| 29. C4×C7⋊C8 | C22 | semidirect |
| 35. C2×C7×D4 | C2×C4 | semidirect |
| 46. C2×D28 | C2×C4 | semidirect |
| 55. #1141 | C2×C4 | direct (N × H) |
| 60. C2×C7⋊C8 | C2×C4 | semidirect |
| 65. C2×C4×D4 | D7 | semidirect |
| 82. C7×D4 | C22×C4 | semidirect |
| 87. C2×C4×C7 | D8 | semidirect |
| 98. D28 | C22×C4 | semidirect |
| 101. C7⋊C8 | C22×C4 | semidirect |
| 113. C4×D4 | C2×D7 | semidirect |
| 138. C4×C7 | C2×D8 | semidirect |
| 150. C2×D4 | C4×D7 | semidirect |
| 175. C2×C7 | C4×D8 | semidirect |
| 194. D4 | C2×C4×D7 | semidirect |
| 202. C2×C4 | #1141 | direct (N × H) |
| 211. C7 | C2×C4×D8 | semidirect |
| 228. C4 | C2×#1141 | direct (N × H) |
| 233. C2 | C4×#1141 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D4 | 2 |
| C22×#1141 | 2 |
| C2×C4×D28 | 2 |
| C2×#6406 | 2 |
| C4×#1141 | 2 |
| C2×#6383 | 2 |
| C2×#6381 | 2 |
| C2×C4×C7⋊C8 | 2 |
| C2×C4×D8 | 7 |