Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
174 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 66 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. #17989516 | C4 | semidirect |
| 13. C2×#14556497 | C4 | semidirect |
| 14. C2×C32×C73 | C4 | semidirect |
| 81. C73 | #7474 | semidirect |
| 88. C2×C32 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989516 | 2 |
| C2×#17989514 | 2 |
| C2×#17988420 | 2 |
| #7474 | 73 |