Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
502 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 32. C2×Dic292 | C8 | semidirect |
| 53. C2×#10596833 | Q16 | semidirect |
| 137. C73 | #9656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626101 | 2 |
| C2×#17989450 | 2 |
| C2×#17989437 | 2 |
| C2×C8×#10596833 | 2 |
| C2×#17988681 | 2 |
| #9656 | 73 |