Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 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. C22×#1131 | C2 | semidirect |
| 3. C2×C4×C7×C8 | C2 | semidirect |
| 4. C2×(C2×D7)⋊C8 | C2 | semidirect |
| 5. C2×C4⋊(C7⋊C8) | C2 | semidirect |
| 6. #89460 | C2 | direct (N × H) |
| 16. C2×#1131 | C22 | semidirect |
| 19. C4×C7×C8 | C22 | semidirect |
| 20. (C2×D7)⋊C8 | C22 | semidirect |
| 21. C4⋊(C7⋊C8) | C22 | semidirect |
| 35. C2×C7×C8 | D4 | semidirect |
| 50. C2×C4×C8 | D7 | semidirect |
| 57. C2×C4×C7 | M16 | semidirect |
| 71. C7×C8 | C2×D4 | semidirect |
| 87. C4×C8 | C2×D7 | semidirect |
| 98. C4×C7 | C2×M16 | semidirect |
| 117. C2×C8 | D28 | semidirect |
| 124. C2×C7 | #436 | semidirect |
| 141. C2×C4 | #1131 | semidirect |
| 150. C8 | C2×D28 | semidirect |
| 151. C7 | C2×#436 | semidirect |
| 163. C4 | C2×#1131 | semidirect |
| 167. C2 | #89460 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1131 | 2 |
| C2×C4×D28 | 2 |
| C2×C4×C7×C8 | 2 |
| C2×(C2×D7)⋊C8 | 2 |
| C2×C4⋊(C7⋊C8) | 2 |
| #89460 | 2 |
| C2×#436 | 7 |