Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
354 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 11. #17985721 | C4 | semidirect |
| 12. C8×C71⋊C8 | C4 | semidirect |
| 24. C8×Dic71 | C8 | semidirect |
| 89. C71 | #8137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588028 | 2 |
| #22586624 | 2 |
| #22586171 | 2 |
| #22586168 | 2 |
| C71×#1275 | 2 |
| #8137 | 71 |