Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23750176 | C2 | semidirect |
| 2. C4×#14558737 | C2 | semidirect |
| 3. #23749951 | C2 | semidirect |
| 4. #23749902 | C2 | semidirect |
| 5. #23749825 | C2 | semidirect |
| 6. #23749821 | C2 | semidirect |
| 7. #23749773 | C2 | semidirect |
| 8. #23749736 | C2 | semidirect |
| 9. #23749728 | C2 | semidirect |
| 10. #23749681 | C2 | semidirect |
| 11. #475×C149 | C2 | semidirect |
| 93. D596 | #41 | semidirect |
| 109. Q8×C149 | #41 | semidirect |
| 144. C149 | #3115 | semidirect |
| 149. #475 | D149 | semidirect |
| 233. Q8 | #14558737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750176 | 2 |
| C4×#14558737 | 2 |
| #23749951 | 2 |
| #23749902 | 2 |
| #23749825 | 2 |
| #23749821 | 2 |
| #23749773 | 2 |
| #23749736 | 2 |
| #23749728 | 2 |
| #23749681 | 2 |
| #475×C149 | 2 |
| #3115 | 149 |