Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 152 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. #17989428 | C4 | semidirect |
| 7. C8×#10596833 | C4 | semidirect |
| 23. #14556501 | C8 | semidirect |
| 32. #97×C73 | C8 | semidirect |
| 96. C73 | #8138 | semidirect |
| 118. #97 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625134 | 2 |
| #22624757 | 2 |
| #22624755 | 2 |
| #22609619 | 2 |
| #8138 | 73 |