Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
434 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #22588388 | C2 | semidirect |
| 4. #22588384 | C2 | semidirect |
| 5. #22586470 | C2 | semidirect |
| 6. #22586468 | C2 | semidirect |
| 9. C23×C71⋊C8 | C4 | semidirect |
| 16. #17986026 | C4 | semidirect |
| 20. #17985963 | C4 | semidirect |
| 21. #17985955 | C4 | semidirect |
| 215. C71 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597035 | 2 |
| #22589981 | 2 |
| #22588388 | 2 |
| #22588384 | 2 |
| #22586470 | 2 |
| #22586468 | 2 |
| C71×#2120 | 2 |
| #12805 | 71 |