Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
392 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23752760 | C2 | semidirect |
| 2. #23752744 | C2 | semidirect |
| 3. #23752514 | C2 | semidirect |
| 4. #23752498 | C2 | semidirect |
| 5. #23752492 | C2 | semidirect |
| 6. #23752462 | C2 | semidirect |
| 7. #23752457 | C2 | semidirect |
| 8. #23752425 | C2 | semidirect |
| 9. #23752409 | C2 | semidirect |
| 10. #23752234 | C2 | semidirect |
| 11. #459×C151 | C2 | semidirect |
| 141. C151 | #3251 | semidirect |
| 152. #459 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752760 | 2 |
| #23752744 | 2 |
| #23752514 | 2 |
| #23752498 | 2 |
| #23752492 | 2 |
| #23752462 | 2 |
| #23752457 | 2 |
| #23752425 | 2 |
| #23752409 | 2 |
| #23752234 | 2 |
| #459×C151 | 2 |
| #3251 | 151 |