Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
158 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 16. C71⋊C32 | Q8 | semidirect |
| 59. C71 | #13733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590615 | 2 |
| #22586541 | 2 |
| C4×C71⋊C32 | 2 |
| C71×#2252 | 2 |
| #13733 | 71 |