Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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. #17989691 | C4 | semidirect |
| 9. C8×#10596842 | C4 | semidirect |
| 25. #14556661 | C8 | semidirect |
| 35. #14556523 | C8 | semidirect |
| 36. #106×C73 | C8 | semidirect |
| 105. C73 | #7180 | semidirect |
| 129. #106 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627125 | 2 |
| #22627040 | 2 |
| #22625734 | 2 |
| #7180 | 73 |