Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
318 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 35. #14556064 | Q8 | semidirect |
| 51. M32×C71 | Q8 | semidirect |
| 55. C2×C16×C71 | Q8 | semidirect |
| 141. C71 | #13455 | semidirect |
| 172. M32 | Dic142 | semidirect |
| 176. C2×C16 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598879 | 2 |
| #22590128 | 2 |
| C2×#17985825 | 2 |
| #22589125 | 2 |
| #22586449 | 2 |
| #22586436 | 2 |
| C71×#1379 | 2 |
| #13455 | 71 |