Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
500 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 28. #17988630 | C4 | semidirect |
| 29. #17988629 | C4 | semidirect |
| 30. #17988596 | C4 | semidirect |
| 32. #419×C73 | C4 | semidirect |
| 233. C73 | #9363 | semidirect |
| 243. #419 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626441 | 2 |
| #22626120 | 2 |
| #22625839 | 2 |
| #22625331 | 2 |
| #22624831 | 2 |
| #22624811 | 2 |
| #22619877 | 2 |
| #9363 | 73 |