Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
372 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 180. C71 | #7709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596719 | 2 |
| #22588455 | 2 |
| #22588087 | 2 |
| #22586166 | 2 |
| #22586164 | 2 |
| #22586162 | 2 |
| C71×#1272 | 2 |
| #7709 | 71 |