Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
218 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 37. C7×Q16 | C16 | semidirect |
| 51. C7⋊C16 | Q16 | direct (N × H) |
| 99. Q16 | C7⋊C16 | direct (N × H) |
| 131. C7 | C16×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C8×Q16 | 2 |
| Q8×C7⋊C16 | 2 |
| Q8⋊(C7⋊C16) | 2 |
| #11725246 | 2 |
| C8×C7⋊C16 | 2 |
| C16×Q16 | 7 |