Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
158 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 18. C71⋊C32 | Q8 | semidirect |
| 21. C32×C71 | Q8 | semidirect |
| 57. C71 | #13731 | semidirect |
| 73. C32 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590614 | 2 |
| #22586540 | 2 |
| #22586539 | 2 |
| C32×Dic71 | 2 |
| C71×#1423 | 2 |
| #13731 | 71 |