Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
574 conjugacy classes of subgroups; only the 260 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 260 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. #17989429 | C4 | semidirect |
| 12. C8×#10596833 | C4 | semidirect |
| 15. C8×#10596831 | C4 | semidirect |
| 16. C8×#10596831 | C4 | semidirect |
| 17. C82×C73 | C4 | semidirect |
| 25. C8×#64408 | C8 | semidirect |
| 85. C73 | #7841 | semidirect |
| 97. C82 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625644 | 2 |
| C4×C8×#64408 | 2 |
| #22625127 | 2 |
| C8×#11924036 | 2 |
| C82×D73 | 2 |
| #7841 | 73 |