Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
518 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 212 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. #17989428 | C4 | semidirect |
| 12. C8×#10596833 | C4 | semidirect |
| 15. #17988309 | C4 | semidirect |
| 16. #17988308 | C4 | semidirect |
| 17. #322×C73 | C4 | semidirect |
| 85. C73 | #7844 | semidirect |
| 96. #322 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625644 | 2 |
| C4×#14556645 | 2 |
| #22625125 | 2 |
| C8×#11924036 | 2 |
| #322×D73 | 2 |
| #7844 | 73 |