Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
674 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
|---|---|---|
| 21. #17988985 | C4 | semidirect |
| 22. #17988984 | C4 | semidirect |
| 23. #17988983 | C4 | semidirect |
| 26. #498×C73 | C4 | semidirect |
| 135. C73 | #22253 | semidirect |
| 140. #498 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626426 | 2 |
| #22626115 | 2 |
| #22625994 | 2 |
| #22625993 | 2 |
| #22625853 | 2 |
| #22625649 | 2 |
| #498×D73 | 2 |
| #22253 | 73 |