Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 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 |
|---|---|---|
| 1. #22591146 | C2 | semidirect |
| 3. #22586942 | C2 | semidirect |
| 5. #22586206 | C2 | semidirect |
| 6. #22586195 | C2 | semidirect |
| 25. #501×C71 | C4 | semidirect |
| 26. #490×C71 | C4 | semidirect |
| 205. C71 | #9382 | semidirect |
| 208. #501 | Dic71 | semidirect |
| 209. #490 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22591146 | 2 |
| #22589260 | 2 |
| #22586942 | 2 |
| #22586887 | 2 |
| #22586206 | 2 |
| #22586195 | 2 |
| C71×#3234 | 2 |
| #9382 | 71 |