Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
206 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 91 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 | #11765855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590248 | 2 |
| C8×#11765855 | 2 |
| #22586409 | 2 |
| Q8⋊(C71⋊C16) | 2 |
| #22586318 | 2 |
| #22586256 | 2 |
| Q8×C16×C71 | 2 |
| #12053 | 71 |