Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
366 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23752768 | C2 | semidirect |
| 3. #23752618 | C2 | semidirect |
| 4. #23752578 | C2 | semidirect |
| 5. #23752577 | C2 | semidirect |
| 6. #23752539 | C2 | semidirect |
| 7. #23752538 | C2 | semidirect |
| 8. #23752501 | C2 | semidirect |
| 9. #23752491 | C2 | semidirect |
| 10. #23752267 | C2 | semidirect |
| 11. #501×C151 | C2 | semidirect |
| 128. C151 | #3235 | semidirect |
| 133. #501 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752768 | 2 |
| #23752763 | 2 |
| #23752618 | 2 |
| #23752578 | 2 |
| #23752577 | 2 |
| #23752539 | 2 |
| #23752538 | 2 |
| #23752501 | 2 |
| #23752491 | 2 |
| #23752267 | 2 |
| #501×C151 | 2 |
| #3235 | 151 |