Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
334 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #22608105 | C2 | semidirect |
| 5. #17989144 | C4 | semidirect |
| 8. #17988941 | C4 | semidirect |
| 13. C4×#11924012 | C4 | semidirect |
| 23. #14556583 | C2×C4 | semidirect |
| 34. C4×#10596831 | C2×C4 | semidirect |
| 141. C73 | #13603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620317 | 2 |
| C2×#17988384 | 2 |
| #22608105 | 2 |
| C2×#354×C73 | 2 |
| #13603 | 73 |