Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
532 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. #22625331 | C2 | semidirect |
| 4. #22624778 | C2 | semidirect |
| 16. #17988519 | C4 | semidirect |
| 18. #17988512 | C4 | semidirect |
| 19. #17988506 | C4 | semidirect |
| 24. #393×C73 | C4 | semidirect |
| 190. C73 | #9183 | semidirect |
| 203. #393 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626784 | 2 |
| #22625678 | 2 |
| #22625331 | 2 |
| #22624778 | 2 |
| #22615854 | 2 |
| #9183 | 73 |