Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
974 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 974 conjugacy classes of subgroups — too many to draw. Only its 226 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. #22626833 | C2 | semidirect |
| 2. #22626371 | C2 | semidirect |
| 4. #22625323 | C2 | semidirect |
| 5. #22625314 | C2 | semidirect |
| 21. #17989316 | C4 | semidirect |
| 22. #17989312 | C4 | semidirect |
| 23. #17989307 | C4 | semidirect |
| 31. D4×Q8×C73 | C4 | semidirect |
| 186. C73 | #17549 | semidirect |
| 192. D4×Q8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626833 | 2 |
| #22626371 | 2 |
| #22625333 | 2 |
| #22625323 | 2 |
| #22625314 | 2 |
| #22625302 | 2 |
| #22624022 | 2 |
| #17549 | 73 |