Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #23749963 | C2 | semidirect |
| 3. #23749917 | C2 | semidirect |
| 4. #23749912 | C2 | semidirect |
| 5. #23749832 | C2 | semidirect |
| 6. #23749827 | C2 | semidirect |
| 8. #23749730 | C2 | semidirect |
| 9. #23749723 | C2 | semidirect |
| 10. #23749682 | C2 | semidirect |
| 11. #533×C149 | C2 | semidirect |
| 136. C149 | #3116 | semidirect |
| 138. #533 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14558736 | 2 |
| #23749963 | 2 |
| #23749917 | 2 |
| #23749912 | 2 |
| #23749832 | 2 |
| #23749827 | 2 |
| #23749785 | 2 |
| #23749730 | 2 |
| #23749723 | 2 |
| #23749682 | 2 |
| #533×C149 | 2 |
| #3116 | 149 |