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. #22618381 | C2 | semidirect |
| 3. #22609874 | C2 | semidirect |
| 4. #22608448 | C2 | semidirect |
| 5. #22608292 | C2 | semidirect |
| 6. #22607778 | C2 | semidirect |
| 7. C73×#1293 | C2 | semidirect |
| 9. C22×#11924017 | C4 | semidirect |
| 10. C22×D584 | C4 | semidirect |
| 19. C2×#14556516 | C4 | semidirect |
| 20. C2×#14556513 | C4 | semidirect |
| 287. #1293 | 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×#17988734 | 2 |
| #22618381 | 2 |
| #22609874 | 2 |
| #22608448 | 2 |
| #22608292 | 2 |
| #22607778 | 2 |
| C73×#1293 | 2 |
| #9241 | 73 |