Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
310 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 36. C2×C71⋊C16 | Q8 | semidirect |
| 38. #14556064 | Q8 | semidirect |
| 51. M32×C71 | Q8 | semidirect |
| 133. C71 | #13460 | semidirect |
| 166. M32 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598868 | 2 |
| #22590114 | 2 |
| #22589128 | 2 |
| #22586455 | 2 |
| #22586438 | 2 |
| #22586427 | 2 |
| C2×#365×C71 | 2 |
| #13460 | 71 |