Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
| 2. C22×#1142 | C2 | semidirect |
| 4. C2×#6438 | C2 | semidirect |
| 5. #89788 | C2 | direct (N × H) |
| 6. C2×#6384 | C2 | semidirect |
| 7. C2×#6383 | C2 | semidirect |
| 8. C2×C4⋊(C7⋊C8) | C2 | semidirect |
| 14. C4×C7×D4 | C22 | semidirect |
| 19. C2×#1142 | C22 | semidirect |
| 27. #6438 | C22 | semidirect |
| 28. #6384 | C22 | semidirect |
| 29. #6383 | C22 | semidirect |
| 30. C4⋊(C7⋊C8) | C22 | semidirect |
| 69. C2×C4×D4 | D7 | semidirect |
| 120. C4×D4 | C2×D7 | semidirect |
| 183. C2×C7 | #463 | semidirect |
| 221. C7 | C2×#463 | semidirect |
| 243. C2 | #89788 | 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×#1142 | 2 |
| C22×#1141 | 2 |
| C2×#6438 | 2 |
| #89788 | 2 |
| C2×#6384 | 2 |
| C2×#6383 | 2 |
| C2×C4⋊(C7⋊C8) | 2 |
| C2×#463 | 7 |