Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
474 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 179. C71 | #9484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597420 | 2 |
| #22593707 | 2 |
| #22588333 | 2 |
| #22586770 | 2 |
| #22586768 | 2 |
| #22586198 | 2 |
| C71×#1286 | 2 |
| #9484 | 71 |