Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
218 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 47. #11924040 | Q16 | semidirect |
| 54. #11924018 | C16 | 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 |
|---|---|
| #22627155 | 2 |
| Q8×#11924040 | 2 |
| #22626996 | 2 |
| #22626986 | 2 |
| Q8⋊#11924040 | 2 |
| C8×#11924040 | 2 |
| #22625518 | 2 |
| C16×Q16 | 73 |