Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
678 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 5. #17989430 | C4 | semidirect |
| 20. C2×C22⋊Dic73 | C8 | semidirect |
| 31. C23×C4×C73 | C8 | semidirect |
| 195. C73 | #7187 | semidirect |
| 211. C23×C4 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989430 | 2 |
| #22608154 | 2 |
| #7187 | 73 |