Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
510 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 3. C2×#64408⋊C16 | C2 | semidirect |
| 4. #22627002 | C2 | semidirect |
| 7. C2×#14556686 | C4 | semidirect |
| 11. C22×#11924040 | C4 | semidirect |
| 12. #17989684 | C4 | semidirect |
| 13. C22⋊#11924040 | C4 | semidirect |
| 49. #11924040 | C22⋊C4 | semidirect |
| 64. C22⋊#64408 | C16 | semidirect |
| 88. C2×#64408 | C2×C16 | semidirect |
| 111. C22×C73 | C4×C16 | semidirect |
| 116. C2×D73 | C4×C16 | semidirect |
| 138. C73 | C16×C22⋊C4 | semidirect |
| 251. C22 | #64408⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556686 | 2 |
| #22627096 | 2 |
| C2×#64408⋊C16 | 2 |
| #22627002 | 2 |
| #22625666 | 2 |
| C16×C22⋊C4 | 73 |