Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23750290 | C2 | semidirect |
| 3. #23749975 | C2 | semidirect |
| 4. #23749965 | C2 | semidirect |
| 5. #23749921 | C2 | semidirect |
| 6. #23749868 | C2 | semidirect |
| 7. #23749762 | C2 | semidirect |
| 8. C4×#14558724 | C2 | semidirect |
| 9. #23749702 | C2 | semidirect |
| 10. #23749632 | C2 | semidirect |
| 11. #461×C149 | C2 | semidirect |
| 126. C149 | #3329 | semidirect |
| 134. #461 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750340 | 2 |
| #23750290 | 2 |
| #23749975 | 2 |
| #23749965 | 2 |
| #23749921 | 2 |
| #23749868 | 2 |
| #23749762 | 2 |
| C4×#14558724 | 2 |
| #23749702 | 2 |
| #23749632 | 2 |
| #461×C149 | 2 |
| #3329 | 149 |