Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23752762 | C2 | semidirect |
| 2. #23752607 | C2 | semidirect |
| 3. #23752602 | C2 | semidirect |
| 4. #23752582 | C2 | semidirect |
| 5. #23752578 | C2 | semidirect |
| 6. #23752434 | C2 | semidirect |
| 7. #23752427 | C2 | semidirect |
| 8. #23752372 | C2 | semidirect |
| 9. #23752355 | C2 | semidirect |
| 10. #23752269 | C2 | semidirect |
| 11. #529×C151 | C2 | semidirect |
| 140. C151 | #3219 | semidirect |
| 143. #529 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752762 | 2 |
| #23752607 | 2 |
| #23752602 | 2 |
| #23752582 | 2 |
| #23752578 | 2 |
| #23752434 | 2 |
| #23752427 | 2 |
| #23752372 | 2 |
| #23752355 | 2 |
| #23752269 | 2 |
| #529×C151 | 2 |
| #3219 | 151 |