Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
174 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 103 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×C7⋊C16 | C2 | semidirect |
| 3. C22⋊(C7⋊C16) | C2 | semidirect |
| 4. C4⋊(C7⋊C16) | C2 | semidirect |
| 5. C4×C7⋊C16 | C2 | semidirect |
| 28. C7⋊C16 | D4 | direct (N × H) |
| 35. C7×D4 | C16 | semidirect |
| 57. C22×C7 | C2×C16 | semidirect |
| 61. C4×C7 | C2×C16 | semidirect |
| 82. D4 | C7⋊C16 | direct (N × H) |
| 93. C7 | D4×C16 | semidirect |
| 96. C22 | C2×C7⋊C16 | semidirect |
| 100. C4 | C2×C7⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C8×D4 | 2 |
| C22×C7⋊C16 | 2 |
| C22⋊(C7⋊C16) | 2 |
| C4⋊(C7⋊C16) | 2 |
| C4×C7⋊C16 | 2 |
| D4×C16 | 7 |