Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
356 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 32. #14556068 | Q8 | semidirect |
| 46. M32×C71 | Q8 | semidirect |
| 48. #107×C71 | Q8 | semidirect |
| 127. C71 | #13457 | semidirect |
| 157. M32 | Dic142 | semidirect |
| 162. #107 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986396 | 2 |
| C2×#17985822 | 2 |
| C2×#17985821 | 2 |
| #22589089 | 2 |
| #22586445 | 2 |
| #22586421 | 2 |
| C71×#1386 | 2 |
| #13457 | 71 |