Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23750173 | C2 | semidirect |
| 2. #23750172 | C2 | semidirect |
| 3. #23749916 | C2 | semidirect |
| 4. #23749915 | C2 | semidirect |
| 5. #23749913 | C2 | semidirect |
| 6. #23749877 | C2 | semidirect |
| 7. #23749875 | C2 | semidirect |
| 8. #23749818 | C2 | semidirect |
| 9. #23749817 | C2 | semidirect |
| 10. #23749647 | C2 | semidirect |
| 11. #459×C149 | C2 | semidirect |
| 150. C149 | #3253 | semidirect |
| 161. #459 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750173 | 2 |
| #23750172 | 2 |
| #23749916 | 2 |
| #23749915 | 2 |
| #23749913 | 2 |
| #23749877 | 2 |
| #23749875 | 2 |
| #23749818 | 2 |
| #23749817 | 2 |
| #23749647 | 2 |
| #459×C149 | 2 |
| #3253 | 149 |