Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
712 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22618377 | C2 | semidirect |
| 3. #22609874 | C2 | semidirect |
| 4. #22608447 | C2 | semidirect |
| 5. #22607807 | C2 | semidirect |
| 6. #22607777 | C2 | semidirect |
| 7. C73×#1471 | C2 | semidirect |
| 9. C22×#11924016 | C4 | semidirect |
| 10. C22×#11924013 | C4 | semidirect |
| 18. C2×#14556514 | C4 | semidirect |
| 19. C2×#14556511 | C4 | semidirect |
| 286. #1471 | D73 | semidirect |
| 289. C73 | #9241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988730 | 2 |
| #22618377 | 2 |
| #22609874 | 2 |
| #22608447 | 2 |
| #22607807 | 2 |
| #22607777 | 2 |
| C73×#1471 | 2 |
| #9241 | 73 |