Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
656 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 213 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×#1132 | C2 | semidirect |
| 3. C2×#6432 | C2 | semidirect |
| 4. C2×C4×C7×C8 | C2 | semidirect |
| 5. #89465 | C2 | direct (N × H) |
| 13. C2×#1132 | C22 | semidirect |
| 17. #6432 | C22 | semidirect |
| 18. C4×C7×C8 | C22 | semidirect |
| 32. C2×C7×C8 | D4 | semidirect |
| 42. C2×C4×C8 | D7 | semidirect |
| 47. C2×C4×C7 | SD16 | semidirect |
| 59. C7×C8 | C2×D4 | semidirect |
| 72. C4×C8 | C2×D7 | semidirect |
| 80. C4×C7 | C2×SD16 | semidirect |
| 96. C2×C8 | D28 | semidirect |
| 101. C2×C7 | #492 | semidirect |
| 116. C2×C4 | #1132 | semidirect |
| 121. C8 | C2×D28 | semidirect |
| 122. C7 | C2×#492 | semidirect |
| 131. C4 | C2×#1132 | semidirect |
| 134. C2 | #89465 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1132 | 2 |
| C2×#6437 | 2 |
| C2×#6432 | 2 |
| C2×C4×C7×C8 | 2 |
| #89465 | 2 |
| C2×#492 | 7 |