Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
410 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 109. C71 | #9801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986404 | 2 |
| #22589329 | 2 |
| #22587099 | 2 |
| #22587024 | 2 |
| C8×M16×C71 | 2 |
| #9801 | 71 |