Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
358 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22590112 | C2 | semidirect |
| 3. C2×#17985821 | C2 | semidirect |
| 6. #22586452 | C2 | semidirect |
| 7. C71×#1386 | C2 | semidirect |
| 9. #17986417 | C4 | semidirect |
| 144. #1386 | D71 | semidirect |
| 145. C71 | #12833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601442 | 2 |
| #22590112 | 2 |
| C2×#17985821 | 2 |
| #22588400 | 2 |
| #22588391 | 2 |
| #22586452 | 2 |
| C71×#1386 | 2 |
| #12833 | 71 |