Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
512 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 94 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. #101×#64408 | C2 | semidirect |
| 4. #22625027 | C2 | semidirect |
| 16. #17989496 | C4 | semidirect |
| 17. #17989495 | C4 | semidirect |
| 21. #17988384 | C4 | semidirect |
| 22. #17988383 | C4 | semidirect |
| 23. #355×C73 | C4 | semidirect |
| 38. #14556652 | C2×C4 | semidirect |
| 53. #14556510 | C2×C4 | semidirect |
| 56. #101×C73 | C2×C4 | semidirect |
| 178. C73 | #12632 | semidirect |
| 195. #355 | #64408 | semidirect |
| 224. #101 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626421 | 2 |
| D73⋊#355 | 2 |
| #101×#64408 | 2 |
| #22625027 | 2 |
| #355×D73 | 2 |
| #12632 | 73 |