Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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. #23752935 | C2 | semidirect |
| 3. #23752563 | C2 | semidirect |
| 4. #23752556 | C2 | semidirect |
| 5. #23752492 | C2 | semidirect |
| 6. #23752452 | C2 | semidirect |
| 7. #23752422 | C2 | semidirect |
| 8. #23752371 | C2 | semidirect |
| 9. C8×D604 | C2 | semidirect |
| 10. #23752205 | C2 | semidirect |
| 11. C4×SD16×C151 | C2 | semidirect |
| 125. C151 | #3302 | semidirect |
| 135. C4×SD16 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752935 | 2 |
| #23752866 | 2 |
| #23752563 | 2 |
| #23752556 | 2 |
| #23752492 | 2 |
| #23752452 | 2 |
| #23752422 | 2 |
| #23752371 | 2 |
| C8×D604 | 2 |
| #23752205 | 2 |
| C4×SD16×C151 | 2 |
| #3302 | 151 |