Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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×D596 | C2 | semidirect |
| 2. #23749984 | C2 | semidirect |
| 3. #23749971 | C2 | semidirect |
| 4. #23749915 | C2 | semidirect |
| 5. #23749910 | C2 | semidirect |
| 6. #23749837 | C2 | semidirect |
| 8. #23749756 | C2 | semidirect |
| 9. #23749735 | C2 | semidirect |
| 10. C4×#14558723 | C2 | semidirect |
| 11. #559×C149 | C2 | semidirect |
| 124. C149 | #3373 | semidirect |
| 126. #559 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D596 | 2 |
| #23749984 | 2 |
| #23749971 | 2 |
| #23749915 | 2 |
| #23749910 | 2 |
| #23749837 | 2 |
| #23749817 | 2 |
| #23749756 | 2 |
| #23749735 | 2 |
| C4×#14558723 | 2 |
| #559×C149 | 2 |
| #3373 | 149 |