Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
206 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 54. C71⋊C16 | Q16 | semidirect |
| 105. C71 | #12054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590249 | 2 |
| #22590245 | 2 |
| C8×#11765855 | 2 |
| #22586409 | 2 |
| #22586320 | 2 |
| C16×C71⋊C8 | 2 |
| C71×Q8⋊C16 | 2 |
| #12054 | 71 |