Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
542 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 141. C71 | #8006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596969 | 2 |
| C2×#17986049 | 2 |
| #22586217 | 2 |
| #22586216 | 2 |
| C71×#1293 | 2 |
| #8006 | 71 |