Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
130 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 19. C7×Q16 | Q8 | semidirect |
| 66. Q16 | Dic14 | semidirect |
| 91. C7 | #2225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×Q16 | 2 |
| #89454 | 2 |
| #89359 | 2 |
| #89285 | 2 |
| C4⋊(C7⋊C16) | 2 |
| #2225 | 7 |