Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
380 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 20. #498×C71 | C4 | semidirect |
| 21. #494×C71 | C4 | semidirect |
| 22. #487×C71 | C4 | semidirect |
| 23. #487×C71 | C4 | semidirect |
| 155. C71 | #9416 | semidirect |
| 158. #498 | Dic71 | semidirect |
| 159. #494 | Dic71 | semidirect |
| 160. #487 | Dic71 | semidirect |
| 161. #487 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597446 | 2 |
| #22586978 | 2 |
| #22586891 | 2 |
| #22586212 | 2 |
| #22586205 | 2 |
| C71×#3185 | 2 |
| #9416 | 71 |