Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 44. #11924018 | C16 | semidirect |
| 54. #11924003 | Q16 | semidirect |
| 105. C73 | C16×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924003 | 2 |
| #22611833 | 2 |
| C8×#11924018 | 2 |
| #22608000 | 2 |
| #22607911 | 2 |
| C16×#10596831 | 2 |
| C73×Q8⋊C16 | 2 |
| C16×Q16 | 73 |