Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
418 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 161. C71 | #8737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590940 | 2 |
| C2×#17985724 | 2 |
| #22586188 | 2 |
| #22586187 | 2 |
| #22586186 | 2 |
| C71×#1282 | 2 |
| #8737 | 71 |