Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
434 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 434 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. #23752761 | C2 | semidirect |
| 2. #23752760 | C2 | semidirect |
| 3. #23752599 | C2 | semidirect |
| 4. #23752572 | C2 | semidirect |
| 5. #23752571 | C2 | semidirect |
| 6. #23752415 | C2 | semidirect |
| 7. #23752405 | C2 | semidirect |
| 8. #23752356 | C2 | semidirect |
| 9. #23752354 | C2 | semidirect |
| 10. #23752267 | C2 | semidirect |
| 11. #496×C151 | C2 | semidirect |
| 149. C151 | #3214 | semidirect |
| 154. #496 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752761 | 2 |
| #23752760 | 2 |
| #23752599 | 2 |
| #23752572 | 2 |
| #23752571 | 2 |
| #23752415 | 2 |
| #23752405 | 2 |
| #23752356 | 2 |
| #23752354 | 2 |
| #23752267 | 2 |
| #496×C151 | 2 |
| #3214 | 151 |