Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #22618985 | C2 | semidirect |
| 3. #22608436 | C2 | semidirect |
| 4. C2×#17988322 | C2 | semidirect |
| 5. #22608292 | C2 | semidirect |
| 6. #22607773 | C2 | semidirect |
| 7. C73×#1298 | C2 | semidirect |
| 10. #17988923 | C4 | semidirect |
| 12. #17988906 | C4 | semidirect |
| 15. #17988740 | C4 | semidirect |
| 17. #17988723 | C4 | semidirect |
| 251. #1298 | D73 | semidirect |
| 253. C73 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620698 | 2 |
| #22618985 | 2 |
| #22608436 | 2 |
| C2×#17988322 | 2 |
| #22608292 | 2 |
| #22607773 | 2 |
| C73×#1298 | 2 |
| #9264 | 73 |