Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C2×#17986121 | C2 | semidirect |
| 3. #22590069 | C2 | semidirect |
| 4. #22589231 | C2 | semidirect |
| 5. #22586453 | C2 | semidirect |
| 6. #22586423 | C2 | semidirect |
| 7. C71×#2148 | C2 | semidirect |
| 11. #17986439 | C4 | semidirect |
| 13. #17986434 | C4 | semidirect |
| 184. #2148 | D71 | semidirect |
| 189. C71 | #13024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| C2×#17986121 | 2 |
| #22590069 | 2 |
| #22589231 | 2 |
| #22586453 | 2 |
| #22586423 | 2 |
| C71×#2148 | 2 |
| #13024 | 71 |