Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
562 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 96 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. #22626578 | C2 | semidirect |
| 2. #22625439 | C2 | semidirect |
| 3. D73⋊#331 | C2 | semidirect |
| 4. #22625227 | C2 | semidirect |
| 5. #22624821 | C2 | semidirect |
| 6. #22624800 | C2 | semidirect |
| 248. C73 | #9173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626578 | 2 |
| #22625439 | 2 |
| D73⋊#331 | 2 |
| #22625227 | 2 |
| #22624821 | 2 |
| #22624800 | 2 |
| #22619406 | 2 |
| #9173 | 73 |