Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
180 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 12. #125×C71 | C8 | semidirect |
| 71. C71 | #7358 | semidirect |
| 80. #125 | C71⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22586286 | 2 |
| C71×#1992 | 2 |
| #7358 | 71 |