Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23752763 | C2 | semidirect |
| 2. #23752747 | C2 | semidirect |
| 3. #23752604 | C2 | semidirect |
| 4. #23752601 | C2 | semidirect |
| 5. #23752578 | C2 | semidirect |
| 6. #23752437 | C2 | semidirect |
| 7. #23752430 | C2 | semidirect |
| 8. #23752377 | C2 | semidirect |
| 9. #23752360 | C2 | semidirect |
| 10. #23752267 | C2 | semidirect |
| 11. #491×C151 | C2 | semidirect |
| 140. C151 | #3219 | semidirect |
| 146. #491 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752763 | 2 |
| #23752747 | 2 |
| #23752604 | 2 |
| #23752601 | 2 |
| #23752578 | 2 |
| #23752437 | 2 |
| #23752430 | 2 |
| #23752377 | 2 |
| #23752360 | 2 |
| #23752267 | 2 |
| #491×C151 | 2 |
| #3219 | 151 |