Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23750159 | C2 | semidirect |
| 2. #23750007 | C2 | semidirect |
| 3. #23749979 | C2 | semidirect |
| 4. #23749832 | C2 | semidirect |
| 5. #23749827 | C2 | semidirect |
| 6. #23749822 | C2 | semidirect |
| 7. #23749817 | C2 | semidirect |
| 8. #23749787 | C2 | semidirect |
| 9. #23749770 | C2 | semidirect |
| 10. #23749678 | C2 | semidirect |
| 11. #532×C149 | C2 | semidirect |
| 144. C149 | #3212 | semidirect |
| 146. #532 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750159 | 2 |
| #23750007 | 2 |
| #23749979 | 2 |
| #23749832 | 2 |
| #23749827 | 2 |
| #23749822 | 2 |
| #23749817 | 2 |
| #23749787 | 2 |
| #23749770 | 2 |
| #23749678 | 2 |
| #532×C149 | 2 |
| #3212 | 149 |