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. #22609742 | C2 | semidirect |
| 4. #22608522 | C2 | semidirect |
| 5. #22608438 | C2 | semidirect |
| 6. #22607802 | C2 | semidirect |
| 7. C73×#1300 | C2 | semidirect |
| 11. #17988873 | C4 | semidirect |
| 12. #17988868 | C4 | semidirect |
| 13. #17988788 | C4 | semidirect |
| 14. #17988783 | C4 | semidirect |
| 208. #1300 | 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 |
|---|---|
| #22620083 | 2 |
| #22618946 | 2 |
| #22609742 | 2 |
| #22608522 | 2 |
| #22608438 | 2 |
| #22607802 | 2 |
| C73×#1300 | 2 |
| #9161 | 73 |