Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
438 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23750175 | C2 | semidirect |
| 2. #23750001 | C2 | semidirect |
| 3. #23749999 | C2 | semidirect |
| 4. #23749975 | C2 | semidirect |
| 5. #23749971 | C2 | semidirect |
| 6. #23749837 | C2 | semidirect |
| 7. #23749770 | C2 | semidirect |
| 8. #23749678 | C2 | semidirect |
| 9. #532×C149 | C2 | semidirect |
| 120. C149 | #3207 | semidirect |
| 123. #532 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| #23750001 | 2 |
| #23749999 | 2 |
| #23749975 | 2 |
| #23749971 | 2 |
| #23749837 | 2 |
| #23749770 | 2 |
| #23749678 | 2 |
| #532×C149 | 2 |
| #3207 | 149 |