Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
810 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 176 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. #22626658 | C2 | semidirect |
| 2. #22626067 | C2 | semidirect |
| 3. #22625921 | C2 | semidirect |
| 4. #22625856 | C2 | semidirect |
| 5. #22625649 | C2 | semidirect |
| 18. #17988972 | C4 | semidirect |
| 19. #17988964 | C4 | semidirect |
| 20. #17988961 | C4 | semidirect |
| 22. #494×C73 | C4 | semidirect |
| 120. C73 | #22282 | semidirect |
| 125. #494 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626658 | 2 |
| #22626067 | 2 |
| #22625921 | 2 |
| #22625856 | 2 |
| #22625649 | 2 |
| #22620360 | 2 |
| #22282 | 73 |