Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 163 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×#17989027 | C2 | semidirect |
| 2. C22×#14556536 | C2 | semidirect |
| 4. #22618798 | C2 | semidirect |
| 5. #22611996 | C2 | semidirect |
| 6. #22611970 | C2 | semidirect |
| 7. #22611689 | C2 | semidirect |
| 8. #22611646 | C2 | semidirect |
| 9. C73×#2138 | C2 | semidirect |
| 16. C2×#14556537 | C22 | semidirect |
| 19. C2×#14556535 | C22 | semidirect |
| 25. #17988681 | C22 | semidirect |
| 28. #17988405 | C22 | semidirect |
| 33. #358×C73 | C22 | semidirect |
| 34. #357×C73 | C22 | semidirect |
| 40. C2×Dic292 | D4 | semidirect |
| 185. #2138 | D73 | semidirect |
| 186. C73 | #33587 | semidirect |
| 209. #358 | C2×D73 | semidirect |
| 211. #357 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989027 | 2 |
| C22×#14556536 | 2 |
| #22620418 | 2 |
| #22618798 | 2 |
| #22611996 | 2 |
| #22611970 | 2 |
| #22611689 | 2 |
| #22611646 | 2 |
| C73×#2138 | 2 |
| #33587 | 73 |