Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
364 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 163. C71 | #10555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589115 | 2 |
| #22587030 | 2 |
| #22587025 | 2 |
| C2×#17985748 | 2 |
| #22586743 | 2 |
| #22586191 | 2 |
| C71×#3165 | 2 |
| #10555 | 71 |