Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 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. #23749991 | C2 | semidirect |
| 3. #23749973 | C2 | semidirect |
| 4. #23749922 | C2 | semidirect |
| 5. #23749902 | C2 | semidirect |
| 6. #23749825 | C2 | semidirect |
| 7. #23749825 | C2 | semidirect |
| 8. #23749756 | C2 | semidirect |
| 9. #23749723 | C2 | semidirect |
| 10. C4×#14558723 | C2 | semidirect |
| 11. #557×C149 | C2 | semidirect |
| 93. Q8×C149 | #41 | semidirect |
| 124. C149 | #3368 | semidirect |
| 126. #557 | D149 | semidirect |
| 204. Q8 | #14558737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750297 | 2 |
| #23749991 | 2 |
| #23749973 | 2 |
| #23749922 | 2 |
| #23749902 | 2 |
| #23749825 | 2 |
| #23749756 | 2 |
| #23749723 | 2 |
| C4×#14558723 | 2 |
| #557×C149 | 2 |
| #3368 | 149 |