Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. C22×#14558994 | C2 | semidirect |
| 3. #23752786 | C2 | semidirect |
| 4. #23752371 | C2 | semidirect |
| 5. #23752366 | C2 | semidirect |
| 6. #23752222 | C2 | semidirect |
| 7. #23752208 | C2 | semidirect |
| 8. #23752180 | C2 | semidirect |
| 9. C2×#137×C151 | C2 | semidirect |
| 140. C151 | #3011 | semidirect |
| 143. C2×#137 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012786 | 2 |
| C22×#14558994 | 2 |
| #23752786 | 2 |
| #23752371 | 2 |
| #23752366 | 2 |
| #23752222 | 2 |
| #23752208 | 2 |
| #23752180 | 2 |
| C2×#137×C151 | 2 |
| #3011 | 151 |