Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
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 |
|---|---|---|
| 2. Q8×D596 | C2 | semidirect |
| 3. #23749976 | C2 | semidirect |
| 4. #23749969 | C2 | semidirect |
| 5. #23749920 | C2 | semidirect |
| 6. #23749870 | C2 | semidirect |
| 7. #23749830 | C2 | semidirect |
| 8. #23749762 | C2 | semidirect |
| 9. #23749704 | C2 | semidirect |
| 10. #23749632 | C2 | semidirect |
| 11. C4×SD16×C149 | C2 | semidirect |
| 126. C149 | #3329 | semidirect |
| 136. C4×SD16 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750340 | 2 |
| Q8×D596 | 2 |
| #23749976 | 2 |
| #23749969 | 2 |
| #23749920 | 2 |
| #23749870 | 2 |
| #23749830 | 2 |
| #23749762 | 2 |
| #23749704 | 2 |
| #23749632 | 2 |
| C4×SD16×C149 | 2 |
| #3329 | 149 |