Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
852 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22620738 | C2 | semidirect |
| 2. C2×#17988738 | C2 | semidirect |
| 4. #22608296 | C2 | semidirect |
| 5. #22608292 | C2 | semidirect |
| 6. #22607818 | C2 | semidirect |
| 7. C73×#1783 | C2 | semidirect |
| 235. #1783 | D73 | semidirect |
| 239. C73 | #9987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620738 | 2 |
| C2×#17988738 | 2 |
| C2×#17988721 | 2 |
| #22608296 | 2 |
| #22608292 | 2 |
| #22607818 | 2 |
| C73×#1783 | 2 |
| #9987 | 73 |