Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 1. C2×C7×C4⋊Q8 | C2 | semidirect |
| 3. #89856 | C2 | direct (N × H) |
| 5. C2×#6382 | C2 | semidirect |
| 6. C2×C4⋊(C7⋊C8) | C2 | semidirect |
| 11. C7×C4⋊Q8 | C22 | semidirect |
| 21. #6382 | C22 | semidirect |
| 22. C4⋊(C7⋊C8) | C22 | semidirect |
| 34. C2×D28 | Q8 | semidirect |
| 48. C2×C4⋊Q8 | D7 | semidirect |
| 74. D28 | C2×Q8 | semidirect |
| 82. C4⋊Q8 | C2×D7 | semidirect |
| 132. C2×C7 | #476 | semidirect |
| 160. C7 | C2×#476 | semidirect |
| 177. C2 | #89856 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C4⋊Q8 | 2 |
| C2×C4×D28 | 2 |
| #89856 | 2 |
| C2×#6383 | 2 |
| C2×#6382 | 2 |
| C2×C4⋊(C7⋊C8) | 2 |
| C2×#476 | 7 |