Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
500 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 297 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 |
|---|---|---|
| 2. C2×C22⋊(C7⋊C8) | C2 | semidirect |
| 3. D4×C7⋊C8 | C2 | semidirect |
| 4. #89697 | C2 | semidirect |
| 12. C22×C7⋊C8 | C22 | semidirect |
| 14. C22⋊(C7⋊C8) | C22 | semidirect |
| 15. C4⋊(C7⋊C8) | C22 | semidirect |
| 16. C4×C7⋊C8 | C22 | semidirect |
| 19. C2×C7×D4 | C8 | semidirect |
| 40. C23×C7 | C2×C8 | semidirect |
| 43. C7×D4 | C2×C8 | semidirect |
| 49. C2×C4×C7 | C2×C8 | semidirect |
| 82. C2×D4 | C7⋊C8 | semidirect |
| 104. C23 | C2×C7⋊C8 | semidirect |
| 107. D4 | C2×C7⋊C8 | semidirect |
| 113. C2×C4 | C2×C7⋊C8 | semidirect |
| 120. C7 | #2972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D4 | 2 |
| C2×C22⋊(C7⋊C8) | 2 |
| D4×C7⋊C8 | 2 |
| #89697 | 2 |
| #2972 | 7 |