Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 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. #23752767 | C2 | semidirect |
| 3. #23752604 | C2 | semidirect |
| 4. #23752572 | C2 | semidirect |
| 5. #23752571 | C2 | semidirect |
| 6. #23752420 | C2 | semidirect |
| 7. #23752410 | C2 | semidirect |
| 8. #23752373 | C2 | semidirect |
| 9. #23752371 | C2 | semidirect |
| 10. #23752267 | C2 | semidirect |
| 11. #497×C151 | C2 | semidirect |
| 141. C151 | #3216 | semidirect |
| 146. #497 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752767 | 2 |
| #23752761 | 2 |
| #23752604 | 2 |
| #23752572 | 2 |
| #23752571 | 2 |
| #23752420 | 2 |
| #23752410 | 2 |
| #23752373 | 2 |
| #23752371 | 2 |
| #23752267 | 2 |
| #497×C151 | 2 |
| #3216 | 151 |