Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
274 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 7. #17989509 | C4 | semidirect |
| 9. C8×#10596833 | C4 | semidirect |
| 24. #14556525 | C8 | semidirect |
| 35. #108×C73 | C8 | semidirect |
| 102. C73 | #7179 | semidirect |
| 124. #108 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989509 | 2 |
| C2×C8×#10596833 | 2 |
| #22609813 | 2 |
| #7179 | 73 |