Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 286 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. #22590152 | C2 | semidirect |
| 3. #22586333 | C2 | semidirect |
| 5. #22586327 | C2 | semidirect |
| 7. C71×#1841 | C2 | semidirect |
| 9. #17986401 | C4 | semidirect |
| 10. #17986383 | C4 | semidirect |
| 15. #17986112 | C4 | semidirect |
| 16. #17986107 | C4 | semidirect |
| 142. #1841 | D71 | semidirect |
| 147. C71 | #11836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599069 | 2 |
| #22590152 | 2 |
| #22586333 | 2 |
| #22586330 | 2 |
| #22586327 | 2 |
| #22586324 | 2 |
| C71×#1841 | 2 |
| #11836 | 71 |