Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 21. #500×C71 | C4 | semidirect |
| 22. #498×C71 | C4 | semidirect |
| 150. C71 | #9427 | semidirect |
| 154. #500 | Dic71 | semidirect |
| 155. #498 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22591521 | 2 |
| #22587057 | 2 |
| #22586891 | 2 |
| #22586205 | 2 |
| C71×#3165 | 2 |
| #9427 | 71 |