Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
242 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 16. #14556664 | C8 | semidirect |
| 21. C2×#11924003 | C8 | semidirect |
| 24. C2×C16×C73 | C8 | semidirect |
| 89. C73 | #7154 | semidirect |
| 107. C2×C16 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989677 | 2 |
| C2×C16×#64408 | 2 |
| #7154 | 73 |