Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 338 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. Q8×Dic298 | C2 | semidirect |
| 4. #23749975 | C2 | semidirect |
| 6. #23749908 | C2 | semidirect |
| 8. #23749752 | C2 | semidirect |
| 9. #23749732 | C2 | semidirect |
| 11. #462×C149 | C2 | semidirect |
| 116. C149 | #3369 | semidirect |
| 125. #462 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic298 | 2 |
| #23750349 | 2 |
| #23749986 | 2 |
| #23749975 | 2 |
| #23749916 | 2 |
| #23749908 | 2 |
| #23749849 | 2 |
| #23749752 | 2 |
| #23749732 | 2 |
| C4×#14558723 | 2 |
| #462×C149 | 2 |
| #3369 | 149 |