Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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. #23750340 | C2 | semidirect |
| 2. #23749975 | C2 | semidirect |
| 3. #23749963 | C2 | semidirect |
| 4. #23749915 | C2 | semidirect |
| 5. #23749856 | C2 | semidirect |
| 6. #23749827 | C2 | semidirect |
| 7. #23749770 | C2 | semidirect |
| 8. C4×#14558721 | C2 | semidirect |
| 9. D4×#11924746 | C2 | semidirect |
| 10. #23749621 | C2 | semidirect |
| 11. #547×C149 | C2 | semidirect |
| 130. C149 | #3303 | semidirect |
| 133. #547 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750340 | 2 |
| #23749975 | 2 |
| #23749963 | 2 |
| #23749915 | 2 |
| #23749856 | 2 |
| #23749827 | 2 |
| #23749770 | 2 |
| C4×#14558721 | 2 |
| D4×#11924746 | 2 |
| #23749621 | 2 |
| #547×C149 | 2 |
| #3303 | 149 |