Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
374 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 12. #17988989 | C4 | semidirect |
| 13. #17988988 | C4 | semidirect |
| 19. #499×C73 | C4 | semidirect |
| 117. C73 | #13284 | semidirect |
| 124. #499 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626132 | 2 |
| #22625867 | 2 |
| #22624988 | 2 |
| #499×D73 | 2 |
| #13284 | 73 |