Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
198 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 49. C71⋊C16 | Q16 | semidirect |
| 102. C71 | #12459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590620 | 2 |
| Q8×C71⋊C16 | 2 |
| #22587744 | 2 |
| #22586413 | 2 |
| #22586399 | 2 |
| #22586395 | 2 |
| C71×#1674 | 2 |
| #12459 | 71 |