Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
308 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
| 52. C2×C16×C71 | Q8 | semidirect |
| 132. C71 | #13269 | semidirect |
| 170. C2×C16 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597280 | 2 |
| #22590105 | 2 |
| #22589944 | 2 |
| #22586427 | 2 |
| #22586425 | 2 |
| #22586420 | 2 |
| C71×#1375 | 2 |
| #13269 | 71 |