Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
206 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 64. C16×C71 | Q16 | semidirect |
| 105. C71 | #12053 | semidirect |
| 162. C16 | Dic284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590248 | 2 |
| C16×Dic142 | 2 |
| C8×Dic284 | 2 |
| #22586410 | 2 |
| #22586320 | 2 |
| C71×#1311 | 2 |
| #12053 | 71 |