Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
306 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 9. #17989516 | C4 | semidirect |
| 10. #17989515 | C4 | semidirect |
| 105. C73 | #12676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989516 | 2 |
| C2×#17989515 | 2 |
| C4×#14556662 | 2 |
| #22624991 | 2 |
| #346×D73 | 2 |
| #12676 | 73 |