Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
352 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 352 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. #23750348 | C2 | semidirect |
| 3. #23750023 | C2 | semidirect |
| 4. #23749964 | C2 | semidirect |
| 5. #23749948 | C2 | semidirect |
| 6. #23749920 | C2 | semidirect |
| 7. #23749905 | C2 | semidirect |
| 8. #23749851 | C2 | semidirect |
| 9. C8×D596 | C2 | semidirect |
| 10. #23749660 | C2 | semidirect |
| 11. C4×SD16×C149 | C2 | semidirect |
| 120. C149 | #3340 | semidirect |
| 130. C4×SD16 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750348 | 2 |
| #23750340 | 2 |
| #23750023 | 2 |
| #23749964 | 2 |
| #23749948 | 2 |
| #23749920 | 2 |
| #23749905 | 2 |
| #23749851 | 2 |
| C8×D596 | 2 |
| #23749660 | 2 |
| C4×SD16×C149 | 2 |
| #3340 | 149 |