Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
412 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 100 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. #22626146 | C2 | semidirect |
| 4. #22625752 | C2 | semidirect |
| 5. #22625009 | C2 | semidirect |
| 6. #22625000 | C2 | semidirect |
| 19. #17989502 | C4 | semidirect |
| 26. #17988403 | C4 | semidirect |
| 27. #17988401 | C4 | semidirect |
| 28. #17988399 | C4 | semidirect |
| 29. #362×C73 | C4 | semidirect |
| 174. C73 | #12651 | semidirect |
| 190. #362 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989633 | 2 |
| #22626247 | 2 |
| #22626146 | 2 |
| #22625752 | 2 |
| #22625009 | 2 |
| #22625000 | 2 |
| #22611679 | 2 |
| #12651 | 73 |