Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
516 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22621322 | C2 | semidirect |
| 3. #22610909 | C2 | semidirect |
| 4. #22610907 | C2 | semidirect |
| 6. #22607844 | C2 | semidirect |
| 215. C73 | #10302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621322 | 2 |
| #22621318 | 2 |
| #22610909 | 2 |
| #22610907 | 2 |
| #22610760 | 2 |
| #22607844 | 2 |
| C73×#3254 | 2 |
| #10302 | 73 |