Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
680 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22586360 | C2 | semidirect |
| 5. C23×Dic142 | C4 | semidirect |
| 10. #17985911 | C4 | semidirect |
| 13. C2×C71⋊#95 | C4 | semidirect |
| 196. C71 | #11808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985911 | 2 |
| #22586667 | 2 |
| #22586360 | 2 |
| C71×#1819 | 2 |
| #11808 | 71 |