Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23752622 | C2 | semidirect |
| 3. #23752602 | C2 | semidirect |
| 4. #23752578 | C2 | semidirect |
| 5. #23752571 | C2 | semidirect |
| 6. #23752463 | C2 | semidirect |
| 7. #23752460 | C2 | semidirect |
| 8. C4×#14558991 | C2 | semidirect |
| 9. C4×#14558989 | C2 | semidirect |
| 10. C4×#14558988 | C2 | semidirect |
| 11. #529×C151 | C2 | semidirect |
| 92. C151⋊C8 | #41 | semidirect |
| 137. C151 | #3171 | semidirect |
| 140. #529 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752762 | 2 |
| #23752622 | 2 |
| #23752602 | 2 |
| #23752578 | 2 |
| #23752571 | 2 |
| #23752463 | 2 |
| #23752460 | 2 |
| C4×#14558991 | 2 |
| C4×#14558989 | 2 |
| C4×#14558988 | 2 |
| #529×C151 | 2 |
| #3171 | 151 |