Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
314 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. #22590113 | C2 | semidirect |
| 4. #22588227 | C2 | semidirect |
| 5. #22586443 | C2 | semidirect |
| 6. #22586423 | C2 | semidirect |
| 21. #362×C71 | C4 | semidirect |
| 22. #361×C71 | C4 | semidirect |
| 146. C71 | #13140 | semidirect |
| 158. #362 | Dic71 | semidirect |
| 159. #361 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590113 | 2 |
| #22590076 | 2 |
| #22589234 | 2 |
| #22588227 | 2 |
| #22586443 | 2 |
| #22586423 | 2 |
| C71×#2148 | 2 |
| #13140 | 71 |