Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1358 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1358 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 9. #543×C71 | C4 | semidirect |
| 16. C23×Dic71 | Q8 | semidirect |
| 20. C2×C22⋊Dic71 | Q8 | semidirect |
| 142. C71 | #11390 | semidirect |
| 145. #543 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985766 | 2 |
| #22586562 | 2 |
| C2×#543×C71 | 2 |
| #11390 | 71 |