Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
366 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. C2×#17988415 | C2 | semidirect |
| 4. #22608041 | C2 | semidirect |
| 5. C2×#368×C73 | C2 | semidirect |
| 8. #17989003 | C4 | semidirect |
| 121. C2×#368 | D73 | semidirect |
| 125. C73 | #12843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989003 | 2 |
| C2×#17988415 | 2 |
| #22609992 | 2 |
| #22608041 | 2 |
| C2×#368×C73 | 2 |
| #12843 | 73 |