Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
634 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 15. C2×#14556523 | C4 | semidirect |
| 16. C2×#14556522 | C4 | semidirect |
| 19. C2×#106×C73 | C4 | semidirect |
| 168. C73 | #11366 | semidirect |
| 178. C2×#106 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625634 | 2 |
| #22625623 | 2 |
| #22625618 | 2 |
| #22625596 | 2 |
| C2×#106×D73 | 2 |
| #11366 | 73 |