Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23750349 | C2 | semidirect |
| 3. #23749973 | C2 | semidirect |
| 4. #23749951 | C2 | semidirect |
| 5. #23749855 | C2 | semidirect |
| 6. #23749826 | C2 | semidirect |
| 7. #23749790 | C2 | semidirect |
| 8. C4×#14558726 | C2 | semidirect |
| 9. #23749690 | C2 | semidirect |
| 10. #23749620 | C2 | semidirect |
| 11. #475×C149 | C2 | semidirect |
| 127. C149 | #3304 | semidirect |
| 133. #475 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750349 | 2 |
| #23750297 | 2 |
| #23749973 | 2 |
| #23749951 | 2 |
| #23749855 | 2 |
| #23749826 | 2 |
| #23749790 | 2 |
| C4×#14558726 | 2 |
| #23749690 | 2 |
| #23749620 | 2 |
| #475×C149 | 2 |
| #3304 | 149 |