Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
210 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 107. C71 | #12076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22587237 | 2 |
| Q16×C71⋊C8 | 2 |
| #22586414 | 2 |
| #22586304 | 2 |
| #22586259 | 2 |
| C4×Q32×C71 | 2 |
| #12076 | 71 |