Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
712 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#17989028 | C2 | semidirect |
| 3. #22618799 | C2 | semidirect |
| 4. #22611991 | C2 | semidirect |
| 5. #22611969 | C2 | semidirect |
| 6. #22611689 | C2 | semidirect |
| 7. #22611647 | C2 | semidirect |
| 8. #22611639 | C2 | semidirect |
| 9. C22×SD32×C73 | C2 | semidirect |
| 15. C2×#14556537 | C22 | semidirect |
| 16. C2×#14556534 | C22 | semidirect |
| 22. Q16×Dic73 | C22 | semidirect |
| 26. #17988405 | C22 | semidirect |
| 27. #17988392 | C22 | semidirect |
| 28. #17988389 | C22 | semidirect |
| 67. C2×Q16×C73 | D4 | semidirect |
| 178. C22×SD32 | D73 | semidirect |
| 186. C73 | #33587 | semidirect |
| 221. C2×Q16 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989028 | 2 |
| #22620412 | 2 |
| #22618799 | 2 |
| #22611991 | 2 |
| #22611969 | 2 |
| #22611689 | 2 |
| #22611647 | 2 |
| #22611639 | 2 |
| C22×SD32×C73 | 2 |
| #33587 | 73 |