Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #23752563 | C2 | semidirect |
| 4. #23752549 | C2 | semidirect |
| 5. #23752507 | C2 | semidirect |
| 6. #23752452 | C2 | semidirect |
| 7. #23752422 | C2 | semidirect |
| 8. #23752366 | C2 | semidirect |
| 10. #103×D151 | C2 | semidirect |
| 11. C4×Q16×C151 | C2 | semidirect |
| 81. D604 | Q16 | semidirect |
| 122. C151 | #3299 | semidirect |
| 132. C4×Q16 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752922 | 2 |
| Q8×D604 | 2 |
| #23752563 | 2 |
| #23752549 | 2 |
| #23752507 | 2 |
| #23752452 | 2 |
| #23752422 | 2 |
| #23752366 | 2 |
| C8×D604 | 2 |
| #103×D151 | 2 |
| C4×Q16×C151 | 2 |
| #3299 | 151 |