Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
464 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 16. #17985797 | C4 | semidirect |
| 147. C71 | #12631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22591058 | 2 |
| C2×#17985797 | 2 |
| #101×Dic71 | 2 |
| #22586467 | 2 |
| C71×#1394 | 2 |
| #12631 | 71 |