Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
416 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22590005 | C2 | semidirect |
| 3. #22586504 | C2 | semidirect |
| 4. #22586502 | C2 | semidirect |
| 5. C71×#2126 | C2 | semidirect |
| 8. #17986549 | C4 | semidirect |
| 11. #17986378 | C4 | semidirect |
| 13. #17986373 | C4 | semidirect |
| 16. C2×C4×C71⋊C8 | C4 | semidirect |
| 176. #2126 | D71 | semidirect |
| 179. C71 | #13583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598766 | 2 |
| #22590005 | 2 |
| #22586504 | 2 |
| #22586502 | 2 |
| C71×#2126 | 2 |
| #13583 | 71 |