Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
424 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 20. #17985797 | C4 | semidirect |
| 195. C71 | #12971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22591519 | 2 |
| C2×#17985797 | 2 |
| #22588733 | 2 |
| #22588555 | 2 |
| #22586467 | 2 |
| #22586466 | 2 |
| C71×#1857 | 2 |
| #12971 | 71 |