Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#1142 | C2 | semidirect |
| 3. C2×C4×Dic14 | C2 | semidirect |
| 4. C2×#6406 | C2 | semidirect |
| 5. #89847 | C2 | direct (N × H) |
| 6. C2×C4⋊(C7⋊C8) | C2 | semidirect |
| 15. C2×#1142 | C22 | semidirect |
| 21. C4×Dic14 | C22 | semidirect |
| 22. #6406 | C22 | semidirect |
| 23. C4⋊(C7⋊C8) | C22 | semidirect |
| 41. C2×Dic14 | D4 | semidirect |
| 69. C2×C4×C7 | SD16 | semidirect |
| 82. Dic14 | C2×D4 | semidirect |
| 111. C4×C7 | C2×SD16 | semidirect |
| 144. C2×C7 | #460 | semidirect |
| 166. C2×C4 | #1142 | semidirect |
| 174. C7 | C2×#460 | semidirect |
| 186. C4 | C2×#1142 | semidirect |
| 191. C2 | #89847 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#127 | 2 |
| C22×#1142 | 2 |
| C2×C4×Dic14 | 2 |
| C2×#6406 | 2 |
| #89847 | 2 |
| C2×C4⋊(C7⋊C8) | 2 |
| C2×#460 | 7 |