Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
474 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #22618946 | C2 | semidirect |
| 3. #22609744 | C2 | semidirect |
| 4. #22608439 | C2 | semidirect |
| 5. #22607825 | C2 | semidirect |
| 6. #22607803 | C2 | semidirect |
| 7. C73×#1525 | C2 | semidirect |
| 10. #17988869 | C4 | semidirect |
| 11. #17988864 | C4 | semidirect |
| 12. #17988784 | C4 | semidirect |
| 13. #17988779 | C4 | semidirect |
| 206. #1525 | D73 | semidirect |
| 210. C73 | #9161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620076 | 2 |
| #22618946 | 2 |
| #22609744 | 2 |
| #22608439 | 2 |
| #22607825 | 2 |
| #22607803 | 2 |
| C73×#1525 | 2 |
| #9161 | 73 |