Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
586 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22607953 | C2 | semidirect |
| 4. #22607932 | C2 | semidirect |
| 6. C2×#14556570 | C4 | semidirect |
| 8. #17988512 | C4 | semidirect |
| 10. #17988499 | C4 | semidirect |
| 16. C4×C22⋊Dic73 | C4 | semidirect |
| 23. C22×Dic146 | C2×C4 | semidirect |
| 27. C2×C4⋊Dic73 | C2×C4 | semidirect |
| 44. #14556498 | C2×C4 | semidirect |
| 45. #14556498 | C2×C4 | semidirect |
| 221. C73 | #11759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22615089 | 2 |
| C2×#17988354 | 2 |
| #22607953 | 2 |
| #22607932 | 2 |
| C73×#1462 | 2 |
| #11759 | 73 |