Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 120. C71⋊C8 | #101 | semidirect |
| 146. C71 | #9806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986395 | 2 |
| #22589329 | 2 |
| #22587098 | 2 |
| #22587026 | 2 |
| #22587012 | 2 |
| #22586627 | 2 |
| C71×#1966 | 2 |
| #9806 | 71 |