Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
458 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 8. #17986369 | C4 | semidirect |
| 124. C71 | #9004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986369 | 2 |
| #22591526 | 2 |
| #22589313 | 2 |
| #22586222 | 2 |
| C2×#330×C71 | 2 |
| #9004 | 71 |