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. #22618566 | C2 | semidirect |
| 3. #22610006 | C2 | semidirect |
| 5. #22607785 | C2 | semidirect |
| 6. #22607783 | C2 | semidirect |
| 16. #17988490 | C4 | semidirect |
| 17. #17988490 | C4 | semidirect |
| 20. #17988456 | C4 | semidirect |
| 21. #17988452 | C4 | semidirect |
| 243. C73 | #9446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618566 | 2 |
| #22614394 | 2 |
| #22610006 | 2 |
| #22608460 | 2 |
| #22607785 | 2 |
| #22607783 | 2 |
| C73×#1510 | 2 |
| #9446 | 73 |