Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1246 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1246 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 11. C22×#10596842 | Q8 | semidirect |
| 19. C22×Dic146 | C8 | semidirect |
| 23. C22×Q8×C73 | C8 | semidirect |
| 89. C73 | #11380 | semidirect |
| 99. C22×Q8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C2×#10596842)⋊C4 | 2 |
| C22×Q8×#64408 | 2 |
| #11380 | 73 |