Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 296 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 |
|---|---|---|
| 133. C71 | #13473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590135 | 2 |
| #22590105 | 2 |
| C2×#17985815 | 2 |
| #22589256 | 2 |
| #22589128 | 2 |
| #22586443 | 2 |
| C2×#362×C71 | 2 |
| #13473 | 71 |