Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
290 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 76 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. #22626352 | C2 | semidirect |
| 2. C2×#17989515 | C2 | semidirect |
| 3. #22625083 | C2 | semidirect |
| 4. #22625082 | C2 | semidirect |
| 9. #17989518 | C22 | semidirect |
| 11. #17989515 | C22 | semidirect |
| 141. C73 | #13620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626352 | 2 |
| C2×#17989515 | 2 |
| #22625083 | 2 |
| #22625082 | 2 |
| #508×D73 | 2 |
| #13620 | 73 |