Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
486 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 90 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. #22626900 | C2 | semidirect |
| 2. D73⋊#361 | C2 | semidirect |
| 3. #22625816 | C2 | semidirect |
| 4. #22625013 | C2 | semidirect |
| 27. #14556666 | D4 | semidirect |
| 189. C73 | #13079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626900 | 2 |
| D73⋊#361 | 2 |
| #22625816 | 2 |
| #22625013 | 2 |
| #22619577 | 2 |
| #13079 | 73 |