Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 1. #23750176 | C2 | semidirect |
| 2. #23750154 | C2 | semidirect |
| 3. #23750031 | C2 | semidirect |
| 4. #23750015 | C2 | semidirect |
| 5. #23749990 | C2 | semidirect |
| 6. #23749877 | C2 | semidirect |
| 7. #23749874 | C2 | semidirect |
| 8. #23749710 | C2 | semidirect |
| 9. #23749705 | C2 | semidirect |
| 10. #23749577 | C2 | semidirect |
| 11. #489×C149 | C2 | semidirect |
| 100. #11924746 | #41 | semidirect |
| 137. C149 | #3171 | semidirect |
| 144. #489 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750176 | 2 |
| #23750154 | 2 |
| #23750031 | 2 |
| #23750015 | 2 |
| #23749990 | 2 |
| #23749877 | 2 |
| #23749874 | 2 |
| #23749710 | 2 |
| #23749705 | 2 |
| #23749577 | 2 |
| #489×C149 | 2 |
| #3171 | 149 |