Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 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. #23750160 | C2 | semidirect |
| 3. #23750014 | C2 | semidirect |
| 4. #23749991 | C2 | semidirect |
| 5. #23749987 | C2 | semidirect |
| 6. #23749879 | C2 | semidirect |
| 7. #23749872 | C2 | semidirect |
| 8. #23749712 | C2 | semidirect |
| 9. #23749707 | C2 | semidirect |
| 10. #23749577 | C2 | semidirect |
| 11. #501×C149 | C2 | semidirect |
| 110. C8×C149 | #41 | semidirect |
| 137. C149 | #3171 | semidirect |
| 141. #501 | D149 | semidirect |
| 248. C8 | #14558737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750176 | 2 |
| #23750160 | 2 |
| #23750014 | 2 |
| #23749991 | 2 |
| #23749987 | 2 |
| #23749879 | 2 |
| #23749872 | 2 |
| #23749712 | 2 |
| #23749707 | 2 |
| #23749577 | 2 |
| #501×C149 | 2 |
| #3171 | 149 |