Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
248 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 127. C71 | #10689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589064 | 2 |
| #22588480 | 2 |
| #22586243 | 2 |
| #22586236 | 2 |
| #22586235 | 2 |
| #22586170 | 2 |
| C71×#1303 | 2 |
| #10689 | 71 |