Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
878 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 1. #22626253 | C2 | semidirect |
| 2. #22626241 | C2 | semidirect |
| 3. #22626168 | C2 | semidirect |
| 4. #22625813 | C2 | semidirect |
| 20. C2×#14556614 | C4 | semidirect |
| 22. C2×#14556613 | C4 | semidirect |
| 23. C2×Q16×D73 | C4 | semidirect |
| 26. C22×Q16×C73 | C4 | semidirect |
| 230. C73 | #12742 | semidirect |
| 242. C22×Q16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626253 | 2 |
| #22626241 | 2 |
| #22626168 | 2 |
| #22625813 | 2 |
| C2×#17989400 | 2 |
| #12742 | 73 |