Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
274 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 6. #17989692 | C4 | semidirect |
| 9. C8×#10596842 | C4 | semidirect |
| 24. #14556660 | C8 | semidirect |
| 34. #14556527 | C8 | semidirect |
| 36. #108×C73 | C8 | semidirect |
| 105. C73 | #7179 | semidirect |
| 128. #108 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627125 | 2 |
| C2×C8×#10596842 | 2 |
| #22625736 | 2 |
| #7179 | 73 |