Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
636 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 351 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. #22590112 | C2 | semidirect |
| 4. C2×#17985821 | C2 | semidirect |
| 7. #17986416 | C4 | semidirect |
| 20. #14556068 | C2×C4 | semidirect |
| 22. C2×C71⋊C16 | C2×C4 | semidirect |
| 89. C71 | #33404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601443 | 2 |
| #22596951 | 2 |
| #22590112 | 2 |
| C2×#17985821 | 2 |
| C71×#2912 | 2 |
| #33404 | 71 |