Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23750017 | C2 | semidirect |
| 4. #23750014 | C2 | semidirect |
| 5. #23749991 | C2 | semidirect |
| 6. #23749850 | C2 | semidirect |
| 7. #23749843 | C2 | semidirect |
| 8. #23749790 | C2 | semidirect |
| 9. #23749773 | C2 | semidirect |
| 10. #23749680 | C2 | semidirect |
| 11. #491×C149 | C2 | semidirect |
| 140. C149 | #3219 | semidirect |
| 146. #491 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750176 | 2 |
| #23750160 | 2 |
| #23750017 | 2 |
| #23750014 | 2 |
| #23749991 | 2 |
| #23749850 | 2 |
| #23749843 | 2 |
| #23749790 | 2 |
| #23749773 | 2 |
| #23749680 | 2 |
| #491×C149 | 2 |
| #3219 | 149 |