Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
384 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 180. C71 | #8775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22591300 | 2 |
| C4×#14556046 | 2 |
| #22586683 | 2 |
| #22586234 | 2 |
| #22586232 | 2 |
| #22586204 | 2 |
| C71×#1288 | 2 |
| #8775 | 71 |