Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23752769 | C2 | semidirect |
| 2. #23752622 | C2 | semidirect |
| 3. #23752622 | C2 | semidirect |
| 4. #23752571 | C2 | semidirect |
| 5. #23752571 | C2 | semidirect |
| 6. #23752550 | C2 | semidirect |
| 8. #23752519 | C2 | semidirect |
| 9. #23752512 | C2 | semidirect |
| 10. #23752269 | C2 | semidirect |
| 125. C151 | #3240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752769 | 2 |
| #23752622 | 2 |
| #23752571 | 2 |
| #23752550 | 2 |
| #23752533 | 2 |
| #23752519 | 2 |
| #23752512 | 2 |
| #23752269 | 2 |
| #529×C151 | 2 |
| #3240 | 151 |